This study is devoted to a novel fractional friction-damage model for quasi-brittle rock materials subjected to cyclic loadings in the framework of micromechanics.The total damage of material describing the microstruc...This study is devoted to a novel fractional friction-damage model for quasi-brittle rock materials subjected to cyclic loadings in the framework of micromechanics.The total damage of material describing the microstructural degradation is decomposed into two parts:an instantaneous part arising from monotonic loading and a fatigue-related one induced by cyclic loading,relating to the initiation and propagation of microcracks.The inelastic deformation arises directly from frictional sliding along microcracks,inherently coupled with the damage effect.A fractional plastic flow rule is introduced using stress-fractional plasticity operations and covariant transformation approach,instead of classical plastic flow function.Additionally,the progression of fatigue damage is intricately tied to subcracks and can be calculated through application of a convolution law.The number of loading cycles serves as an integration variable,establishing a connection between inelastic deformation and the evolution of fatigue damage.In order to verify the accuracy of the proposed model,comparison between analytical solutions and experimental data are carried out on three different rocks subjected to conventional triaxial compression and cyclic loading tests.The evolution of damage variables is also investigated along with the cumulative deformation and fatigue lifetime.The improvement of the fractional model is finally discussed by comparing with an existing associated fatigue model in literature.展开更多
To investigate the temperature susceptibility and nonlinear memory effects of artificially frozen soil creep behavior,this study conducted uniaxial step-loading creep tests under controlled temperatures ranging from-1...To investigate the temperature susceptibility and nonlinear memory effects of artificially frozen soil creep behavior,this study conducted uniaxial step-loading creep tests under controlled temperatures ranging from-10℃to-20℃.The transient creep characteristics and steady-state creep rates of artificially frozen soils were systematically examined with respect to variations in temperature and stress.Experimental results demonstrate that decreasing temperatures lead to a decaying trend in the steady-state creep rate of silty frozen soil,confirming that low-temperature environments significantly inhibit plastic flow while enhancing material stiffness.Based on fractional calculus theory,a fractional derivative creep model was established.By incorporating temperature dependencies,the model was further improved to account for both stress and temperature effects.The model predictions align closely with experimental data,achieving over 91%agreement(standard deviation±1.8%),and effectively capture the stress-strain behavior of artificially frozen soil under varying thermal conditions.This research provides a reliable theoretical foundation for studying deformation characteristics in cold-regions engineering.展开更多
Fractional differential equations(FDEs)provide a powerful tool for modeling systems with memory and non-local effects,but understanding their underlying structure remains a significant challenge.While numerous numeric...Fractional differential equations(FDEs)provide a powerful tool for modeling systems with memory and non-local effects,but understanding their underlying structure remains a significant challenge.While numerous numerical and semi-analytical methods exist to find solutions,new approaches are needed to analyze the intrinsic properties of the FDEs themselves.This paper introduces a novel computational framework for the structural analysis of FDEs involving iterated Caputo derivatives.The methodology is based on a transformation that recasts the original FDE into an equivalent higher-order form,represented as the sum of a closed-form,integer-order component G(y)and a residual fractional power seriesΨ(x).This transformed FDE is subsequently reduced to a first-order ordinary differential equation(ODE).The primary novelty of the proposed methodology lies in treating the structure of the integer-order component G(y)not as fixed,but as a parameterizable polynomial whose coefficients can be determined via global optimization.Using particle swarm optimization,the framework identifies an optimal ODE architecture by minimizing a dual objective that balances solution accuracy against a high-fidelity reference and the magnitude of the truncated residual series.The effectiveness of the approach is demonstrated on both a linear FDE and a nonlinear fractional Riccati equation.Results demonstrate that the framework successfully identifies an optimal,low-degree polynomial ODE architecture that is not necessarily identical to the forcing function of the original FDE.This work provides a new tool for analyzing the underlying structure of FDEs and gaining deeper insights into the interplay between local and non-local dynamics in fractional systems.展开更多
A novel fractional elastoplastic constitutive model is proposed to accurately characterize the deformation of sandstone under true-triaxial stress states.This model is founded on the yield function and the fractional ...A novel fractional elastoplastic constitutive model is proposed to accurately characterize the deformation of sandstone under true-triaxial stress states.This model is founded on the yield function and the fractional flow rule.The yield function includes parameters that govern the evolution of yield surface,enabling an accurate description of three-dimensional stress states.The direction of plastic flow is governed by the two different fractional orders,which are functions of the plastic internal variable.Additionally,a detailed process is proposed for identifying the yield function parameters and fractional orders.Subsequently,the relationship between the fractional order and the direction of plastic flow in the meridian and deviatoric planes is examined,characterized by the dilation angle and the plastic deflection angle,respectively.The non-orthogonal flow rule,also referred to as the fractional flow rule,allows for a border range of plastic deflection and dilation angles compared to the orthogonal flow rule,thereby significantly enhancing its applicability.The validity and accuracy of proposed model are verified by comparing the analytical solution of the constitutive model with the experimental data.A comparison between the non-orthogonal flow rule and orthogonal flow rule is conducted in both the deviatoric and meridian planes.The further comparison of the stress-strain curves for the non-orthogonal and orthogonal flow rules demonstrates the superiority of the fractional constitutive model.展开更多
This study introduces a novel mathematical model to describe the progression of cholera by integrating fractional derivatives with both singular and non-singular kernels alongside stochastic differential equations ove...This study introduces a novel mathematical model to describe the progression of cholera by integrating fractional derivatives with both singular and non-singular kernels alongside stochastic differential equations over four distinct time intervals.The model incorporates three key fractional derivatives:the Caputo-Fabrizio fractional derivative with a non-singular kernel,the Caputo proportional constant fractional derivative with a singular kernel,and the Atangana-Baleanu fractional derivative with a non-singular kernel.We analyze the stability of the core model and apply various numerical methods to approximate the proposed crossover model.To achieve this,the approximation of Caputo proportional constant fractional derivative with Grünwald-Letnikov nonstandard finite difference method is used for the deterministic model with a singular kernel,while the Toufik-Atangana method is employed for models involving a non-singular Mittag-Leffler kernel.Additionally,the integral Caputo-Fabrizio approximation and a two-step Lagrange polynomial are utilized to approximate the model with a non-singular exponential decay kernel.For the stochastic component,the Milstein method is implemented to approximate the stochastic differential equations.The stability and effectiveness of the proposed model and methodologies are validated through numerical simulations and comparisons with real-world cholera data from Yemen.The results confirm the reliability and practical applicability of the model,providing strong theoretical and empirical support for the approach.展开更多
We propose a fractional-order improved Fitz Hugh–Nagumo(FHN)neuron model in terms of a generalized Caputo fractional derivative.Following the existence of a unique solution for the proposed model,we derive the numeri...We propose a fractional-order improved Fitz Hugh–Nagumo(FHN)neuron model in terms of a generalized Caputo fractional derivative.Following the existence of a unique solution for the proposed model,we derive the numerical solution using a recently proposed L1 predictor–corrector method.The given method is based on the L1-type discretization algorithm and the spline interpolation scheme.We perform the error and stability analyses for the given method.We perform graphical simulations demonstrating that the proposed FHN neuron model generates rich electrical activities of periodic spiking patterns,chaotic patterns,and quasi-periodic patterns.The motivation behind proposing a fractional-order improved FHN neuron model is that such a system can provide a more nuanced description of the process with better understanding and simulation of the neuronal responses by incorporating memory effects and non-local dynamics,which are inherent to many biological systems.展开更多
Being a nonlinear operator,fractional derivatives can affect the enforcement of existence at any given time.As a result,the memory effect has an impact on all nonlinear processes modeled by fractional order differenti...Being a nonlinear operator,fractional derivatives can affect the enforcement of existence at any given time.As a result,the memory effect has an impact on all nonlinear processes modeled by fractional order differential equations(FODEs).The goal of this study is to increase the fractional model of the TB virus’s(FMTBV)accuracy.Stochastic solvers have never been used to solve FMTBV previously.The Bayesian regularized artificial(BRA)method and neural networks(NNs),often referred to as BRA-NNs,were used to solve the FMTBV model.Each scenario features five occurrences that each reflect a different order of derivatives,ranging from 0.8,0.85,0.9,0.95,and 1,as well as five potential rates for different parameters.Training data made up 90%of the data,testing data made up 5%,and validation data made up 5%of the data used to illustrate the FMTBV’s approximations.To verify that the BRA-NNs were correct,the generated simulations were described in the following solutions using the FOLotkaVolterra approach in MATLAB.Comprehensive Simulink results in terms of mean square error,error histogram,and regression analysis investigations further highlight the competence,dependability,and accuracy of the suggested BRA-NNs.展开更多
In 2022,Leukemia is the 13th most common diagnosis of cancer globally as per the source of the International Agency for Research on Cancer(IARC).Leukemia is still a threat and challenge for all regions because of 46.6...In 2022,Leukemia is the 13th most common diagnosis of cancer globally as per the source of the International Agency for Research on Cancer(IARC).Leukemia is still a threat and challenge for all regions because of 46.6%infection in Asia,and 22.1%and 14.7%infection rates in Europe and North America,respectively.To study the dynamics of Leukemia,the population of cells has been divided into three subpopulations of cells susceptible cells,infected cells,and immune cells.To investigate the memory effects and uncertainty in disease progression,leukemia modeling is developed using stochastic fractional delay differential equations(SFDDEs).The feasible properties of positivity,boundedness,and equilibria(i.e.,Leukemia Free Equilibrium(LFE)and Leukemia Present Equilibrium(LPE))of the model were studied rigorously.The local and global stabilities and sensitivity of the parameters around the equilibria under the assumption of reproduction numbers were investigated.To support the theoretical analysis of the model,the Grunwald Letnikov Nonstandard Finite Difference(GL-NSFD)method was used to simulate the results of each subpopulation with memory effect.Also,the positivity and boundedness of the proposed method were studied.Our results show how different methods can help control the cell population and give useful advice to decision-makers on ways to lower leukemia rates in communities.展开更多
Mechanical excavation,blasting,adjacent rockburst and fracture slip that occur during mining excavation impose dynamic loads on the rock mass,leading to further fracture of damaged surrounding rock in three-dimensiona...Mechanical excavation,blasting,adjacent rockburst and fracture slip that occur during mining excavation impose dynamic loads on the rock mass,leading to further fracture of damaged surrounding rock in three-dimensional high-stress and even causing disasters.Therefore,a novel complex true triaxial static-dynamic combined loading method reflecting underground excavation damage and then frequent intermittent disturbance failure is proposed.True triaxial static compression and intermittent disturbance tests are carried out on monzogabbro.The effects of intermediate principal stress and amplitude on the strength characteristics,deformation characteristics,failure characteristics,and precursors of monzogabbro are analyzed,intermediate principal stress and amplitude increase monzogabbro strength and tensile fracture mechanism.Rapid increases in microseismic parameters during rock loading can be precursors for intermittent rock disturbance.Based on the experimental result,the new damage fractional elements and method with considering crack initiation stress and crack unstable stress as initiation and acceleration condition of intermittent disturbance irreversible deformation are proposed.A novel three-dimensional disturbance fractional deterioration model considering the intermediate principal stress effect and intermittent disturbance damage effect is established,and the model predicted results align well with the experimental results.The sensitivity of stress states and model parameters is further explored,and the intermittent disturbance behaviors at different f are predicted.This study provides valuable theoretical bases for the stability analysis of deep mining engineering under dynamic loads.展开更多
Joint time–frequency analysis is an emerging method for interpreting the underlying physics in fuel cells,batteries,and supercapacitors.To increase the reliability of time–frequency analysis,a theoretical correlatio...Joint time–frequency analysis is an emerging method for interpreting the underlying physics in fuel cells,batteries,and supercapacitors.To increase the reliability of time–frequency analysis,a theoretical correlation between frequency-domain stationary analysis and time-domain transient analysis is urgently required.The present work formularizes a thorough model reduction of fractional impedance spectra for electrochemical energy devices involving not only the model reduction from fractional-order models to integer-order models and from high-to low-order RC circuits but also insight into the evolution of the characteristic time constants during the whole reduction process.The following work has been carried out:(i)the model-reduction theory is addressed for typical Warburg elements and RC circuits based on the continued fraction expansion theory and the response error minimization technique,respectively;(ii)the order effect on the model reduction of typical Warburg elements is quantitatively evaluated by time–frequency analysis;(iii)the results of time–frequency analysis are confirmed to be useful to determine the reduction order in terms of the kinetic information needed to be captured;and(iv)the results of time–frequency analysis are validated for the model reduction of fractional impedance spectra for lithium-ion batteries,supercapacitors,and solid oxide fuel cells.In turn,the numerical validation has demonstrated the powerful function of the joint time–frequency analysis.The thorough model reduction of fractional impedance spectra addressed in the present work not only clarifies the relationship between time-domain transient analysis and frequency-domain stationary analysis but also enhances the reliability of the joint time–frequency analysis for electrochemical energy devices.展开更多
This paper develops an Ito-type fractional pathwise integration theory for fractional Brownian motion with Hurst parameters H∈(1/3,1/2],using the Lyons'rough path framework.This approach is designed to fill gaps ...This paper develops an Ito-type fractional pathwise integration theory for fractional Brownian motion with Hurst parameters H∈(1/3,1/2],using the Lyons'rough path framework.This approach is designed to fill gaps in conventional stochastic calculus models that fail to account for temporal persistence prevalent in dynamic systems such as those found in economics,finance,and engineering.The pathwise-defined method not only meets the zero expectation criterion but also addresses the challenges of integrating non-semimartingale processes,which traditional Ito calculus cannot handle.We apply this theory to fractional Black–Scholes models and high-dimensional fractional Ornstein–Uhlenbeck processes,illustrating the advantages of this approach.Additionally,the paper discusses the generalization of It?integrals to rough differential equations(RDE)driven by f BM,emphasizing the necessity of integrand-specific adaptations in the It?rough path lift for stochastic modeling.展开更多
Driven by rapid technological advancements and economic growth,mineral extraction and metal refining have increased dramatically,generating huge volumes of tailings and mine waste(TMWs).Investigating the morphological...Driven by rapid technological advancements and economic growth,mineral extraction and metal refining have increased dramatically,generating huge volumes of tailings and mine waste(TMWs).Investigating the morphological fractions of heavy metals and metalloids(HMMs)in TMWs is key to evaluating their leaching potential into the environment;however,traditional experiments are time-consuming and labor-intensive.In this study,10 machine learning(ML)algorithms were used and compared for rapidly predicting the morphological fractions of HMMs in TMWs.A dataset comprising 2376 data points was used,with mineral composition,elemental properties,and total concentration used as inputs and concentration of morphological fraction used as output.After grid search optimization,the extra tree model performed the best,achieving coefficient of determination(R2)of 0.946 and 0.942 on the validation and test sets,respectively.Electronegativity was found to have the greatest impact on the morphological fraction.The models’performance was enhanced by applying an ensemble method to the top three optimal ML models,including gradient boosting decision tree,extra trees and categorical boosting.Overall,the proposed framework can accurately predict the concentrations of different morphological fractions of HMMs in TMWs.This approach can minimize detection time,aid in the safe management and recovery of TMWs.展开更多
Polydeoxyribonucleotide(PDRN)has been utilized in clinical practice for an extended period;however,its application in the cosmetics is relatively recent.This study aims to explore the research progress of PDRN regardi...Polydeoxyribonucleotide(PDRN)has been utilized in clinical practice for an extended period;however,its application in the cosmetics is relatively recent.This study aims to explore the research progress of PDRN regarding its skin repair and anti-aging properties.To evaluate the potential skin repair,soothing,anti-wrinkle and firming effects of PDRN essence via both in vitro and in vivo test method.This study employed in vitro and in vivo test to assess the skin repair and anti-wrinkle effects.The 3D skin model(FulKutis®)was utilized to verify the effects of the PDRN essence on anti-inflammation,barrier repair,and anti-aging.In human test,a randomized,half-face comparison test with PDRN essence and the placebo was conducted with 33 Chinese subjects who met the test criteria.During the test,the skin conditions in terms of the a*value,facial red area ratio,and Transepidermal Water Loss(TEWL)were evaluated at 30 min,4 h,1 day,and 3 days;the skin conditions in terms of skin elasticity and firmness,skin wrinkles were evaluated at 42 days.Subjects’self-assessments were collected at 3 days and 42 days.The FulKutis■experiments demonstrated that the PDRN essence significantly decreased the levels of IL-1α,TNF-α,and PGE2,and improved the protein levels of Filaggrin,Loricrin,Collagen I,Collagen IV,and the thickness of the epidermal living cell layer.In the human study,the a*value,red area ratio,TEWL,and skin-related parameters(R2,R5,R7,F4,and skin wrinkles)on the test face side exhibited greater improvement compared to the control face side with statistically significant differences.Additionally,subject selfassessments revealed high satisfaction with the PDRN essence.The PDRN essence applied after non-ablative fractional laser treatment promotes barrier repair and soothing effects,shortens the recovery period,and enhances facial firmness and wrinkle improvement at the crow’s feet and undereye regions.No adverse events related to the tested cosmetics were observed.展开更多
The rapid acceleration of global warming and intensifying human activities have exacerbated the fragility and climate sensitivity of ecosystems worldwide,particularly in arid regions.Vegetation,a key component of ecos...The rapid acceleration of global warming and intensifying human activities have exacerbated the fragility and climate sensitivity of ecosystems worldwide,particularly in arid regions.Vegetation,a key component of ecosystems,is critical in enhancing the ecological environment.The Ertix River Basin(ERB)is a transboundary watershed that spans multiple countries,mostly in arid regions.However,research on the fractional vegetation coverage(FVC)and its driving factors in the ERB remains limited.Investigating the spatiotemporal changes in the FVC and its relationship with various factors in the ERB can offer scientific support for optimizing regional vegetation restoration policies and promoting the coordinated development of human-environment interactions.The Moderate-resolution Imaging Spectroradiometer(MODIS)MYD13Q1 V6 data were obtained via the Google Earth Engine platform,and methods including the pixel dichotomy method,Theil-Sen median trend analysis,and Mann‒Kendall test were employed to examine the spatiotemporal dynamics of the FVC in the ERB from 2003 to 2023,with future trend forecast using the Hurst index.The impacts of natural and socioeconomic factors on the FVC were evaluated through the partial least squares-structural equation model(PLS-SEM).The results indicated that the FVC in the ERB showed a slight degradation trend with an average annual decrease of 0.046%during 2003-2023,with significant changes occurring in 2004,2010,and 2019.Spatially,53.380%of the study area was degraded,and the change in the FVC increased gradually from southeast to northwest.The FVC in 63.000%of the study area was highly stable and displayed long-term persistence;and the direct impact of natural factors(path coefficient of 0.617)on the FVC was significantly higher than that of socioeconomic factors(0.167).Among the natural factors,precipitation(0.999)was the most significant.This study reveals the significant impacts of natural and socioeconomic factors on vegetation dynamics in arid regions,and provides a scientific basis for transnational ecological conservation.展开更多
In this study,a numerical method based on the Pell-Lucas polynomials(PLPs)is developed to solve the fractional order HIV/AIDS epidemic model with a treatment compartment.The HIV/AIDS mathematical model with a treatmen...In this study,a numerical method based on the Pell-Lucas polynomials(PLPs)is developed to solve the fractional order HIV/AIDS epidemic model with a treatment compartment.The HIV/AIDS mathematical model with a treatment compartment is divided into five classes,namely,susceptible patients(S),HIV-positive individuals(I),individuals with full-blown AIDS but not receiving ARV treatment(A),individuals being treated(T),and individuals who have changed their sexual habits sufficiently(R).According to the method,by utilizing the PLPs and the collocation points,we convert the fractional order HIV/AIDS epidemic model with a treatment compartment into a nonlinear system of the algebraic equations.Also,the error analysis is presented for the Pell-Lucas approximation method.The aim of this study is to observe the behavior of five populations after 200 days when drug treatment is applied to HIV-infectious and full-blown AIDS people.To demonstrate the usefulness of this method,the applications are made on the numerical example with the help of MATLAB.In addition,four cases of the fractional order derivative(p=1,p=0.95,p=0.9,p=0.85)are examined in the range[0,200].Owing to applications,we figured out that the outcomes have quite decent errors.Also,we understand that the errors decrease when the value of N increases.The figures in this study are created in MATLAB.The outcomes indicate that the presented method is reasonably sufficient and correct.展开更多
In this paper, we consider the Cauchy problem of 3-dimensional tropical climate model. This model reflects the interaction and coupling among the barotropic mode u, the first baroclinic mode v of the velocity and the ...In this paper, we consider the Cauchy problem of 3-dimensional tropical climate model. This model reflects the interaction and coupling among the barotropic mode u, the first baroclinic mode v of the velocity and the temperature θ. The systems with fractional dissipation studied here may arise in the modeling of geophysical circumstances. Mathematically these systems allow simultaneous examination of a family of systems with various levels of regularization. The aim here is the global strong solution with the least dissipation. By energy estimate and delicate analysis, we prove the existence of global solution under three different cases: first, with the help of damping terms, the global strong solution of the system with Λ<sup>2a</sup>u, Λ<sup>2β</sup>v and Λ<sup>2γ</sup> θ for;and second, the global strong solution of the system for with damping terms;finally, the global strong solution of the system for without any damping terms, which improve the known existence theory for this system.展开更多
The outbreak of COVID-19 in 2019 resulted in numerous infections and deaths. In order to better study the transmission of COVID-19, this article adopts an improved fractional-order SIR model. Firstly, the properties o...The outbreak of COVID-19 in 2019 resulted in numerous infections and deaths. In order to better study the transmission of COVID-19, this article adopts an improved fractional-order SIR model. Firstly, the properties of the model are studied, including the feasible domain and bounded solutions of the system. Secondly, the stability of the system is discussed, among other things. Then, the GMMP method is introduced to obtain numerical solutions for the COVID-19 system and combined with the improved MH-NMSS-PSO parameter estimation method to fit the real data of Delhi, India from April 1, 2020 to June 30, 2020. The results show that the fitting effect is quite ideal. Finally, long-term predictions were made on the number of infections. We accurately estimate that the peak number of infections in Delhi, India, can reach around 2.1 million. This paper also compares the fitting performance of the integer-order COVID-19 model and the fractional-order COVID-19 model using the real data from Delhi. The results indicate that the fractional-order model with different orders, as we proposed, performs the best.展开更多
This paper investigates an improved SIR model for COVID-19 based on the Caputo fractional derivative. Firstly, the properties of the model are studied, including the feasible domain and bounded solutions of the system...This paper investigates an improved SIR model for COVID-19 based on the Caputo fractional derivative. Firstly, the properties of the model are studied, including the feasible domain and bounded solutions of the system. Secondly, the stability of the system is discussed, among other things. Then, the GMMP method is introduced to obtain numerical solutions for the COVID-19 system. Numerical simulations were conducted using MATLAB, and the results indicate that our model is valuable for studying virus transmission.展开更多
The fractional calculus approach in the constitutive relationship model of viscoelastic fluid is introduced.The flow near a wall suddenly set in mo- tion is studied for a non-Newtonian viscoelastic fluid with the frac...The fractional calculus approach in the constitutive relationship model of viscoelastic fluid is introduced.The flow near a wall suddenly set in mo- tion is studied for a non-Newtonian viscoelastic fluid with the fractional Maxwell model.Exact solutions of velocity and stress are obtained by using the discrete in- verse Laplace transform of the sequential fractional derivatives.It is found that the effect of the fractional orders in the constitutive relationship on the flow field is signif- icant.The results show that for small times there are appreciable viscoelastic effects on the shear stress at the plate,for large times the viscoelastic effects become weak.展开更多
Many constitutive models exist to characterise the cyclic behaviour of granular soils but can only simulate deformations for very limited cycles. Fractional derivatives have been regarded as one potential instrument f...Many constitutive models exist to characterise the cyclic behaviour of granular soils but can only simulate deformations for very limited cycles. Fractional derivatives have been regarded as one potential instrument for modelling memory-dependent phenomena. In this paper, the physical connection between the fractional derivative order and the fractal dimension of granular soils is investigated in detail. Then a modified elasto-plastic constitutive model is proposed for evaluating the long-term deformation of granular soils under cyclic loading by incorporating the concept of fac- tional calculus. To describe the flow direction of granular soils under cyclic loading, a cyclic flow potential consider- ing particle breakage is used. Test results of several types of granular soils are used to validate the model performance.展开更多
基金Fundamental Research Funds for the Central Universities(Grant No.B230201059)for the support.
文摘This study is devoted to a novel fractional friction-damage model for quasi-brittle rock materials subjected to cyclic loadings in the framework of micromechanics.The total damage of material describing the microstructural degradation is decomposed into two parts:an instantaneous part arising from monotonic loading and a fatigue-related one induced by cyclic loading,relating to the initiation and propagation of microcracks.The inelastic deformation arises directly from frictional sliding along microcracks,inherently coupled with the damage effect.A fractional plastic flow rule is introduced using stress-fractional plasticity operations and covariant transformation approach,instead of classical plastic flow function.Additionally,the progression of fatigue damage is intricately tied to subcracks and can be calculated through application of a convolution law.The number of loading cycles serves as an integration variable,establishing a connection between inelastic deformation and the evolution of fatigue damage.In order to verify the accuracy of the proposed model,comparison between analytical solutions and experimental data are carried out on three different rocks subjected to conventional triaxial compression and cyclic loading tests.The evolution of damage variables is also investigated along with the cumulative deformation and fatigue lifetime.The improvement of the fractional model is finally discussed by comparing with an existing associated fatigue model in literature.
基金National Key Research and Development Program of China“Structural Stability Assessment Techniques and Demonstration for Masonry Ancient Pagodas”(2023YFF0906005)。
文摘To investigate the temperature susceptibility and nonlinear memory effects of artificially frozen soil creep behavior,this study conducted uniaxial step-loading creep tests under controlled temperatures ranging from-10℃to-20℃.The transient creep characteristics and steady-state creep rates of artificially frozen soils were systematically examined with respect to variations in temperature and stress.Experimental results demonstrate that decreasing temperatures lead to a decaying trend in the steady-state creep rate of silty frozen soil,confirming that low-temperature environments significantly inhibit plastic flow while enhancing material stiffness.Based on fractional calculus theory,a fractional derivative creep model was established.By incorporating temperature dependencies,the model was further improved to account for both stress and temperature effects.The model predictions align closely with experimental data,achieving over 91%agreement(standard deviation±1.8%),and effectively capture the stress-strain behavior of artificially frozen soil under varying thermal conditions.This research provides a reliable theoretical foundation for studying deformation characteristics in cold-regions engineering.
基金Research Council of Lithuania(LMTLT),agreement No.S-PD-24-120Research Council of Lithuania(LMTLT),agreement No.S-PD-24-120funded by the Research Council of Lithuania.
文摘Fractional differential equations(FDEs)provide a powerful tool for modeling systems with memory and non-local effects,but understanding their underlying structure remains a significant challenge.While numerous numerical and semi-analytical methods exist to find solutions,new approaches are needed to analyze the intrinsic properties of the FDEs themselves.This paper introduces a novel computational framework for the structural analysis of FDEs involving iterated Caputo derivatives.The methodology is based on a transformation that recasts the original FDE into an equivalent higher-order form,represented as the sum of a closed-form,integer-order component G(y)and a residual fractional power seriesΨ(x).This transformed FDE is subsequently reduced to a first-order ordinary differential equation(ODE).The primary novelty of the proposed methodology lies in treating the structure of the integer-order component G(y)not as fixed,but as a parameterizable polynomial whose coefficients can be determined via global optimization.Using particle swarm optimization,the framework identifies an optimal ODE architecture by minimizing a dual objective that balances solution accuracy against a high-fidelity reference and the magnitude of the truncated residual series.The effectiveness of the approach is demonstrated on both a linear FDE and a nonlinear fractional Riccati equation.Results demonstrate that the framework successfully identifies an optimal,low-degree polynomial ODE architecture that is not necessarily identical to the forcing function of the original FDE.This work provides a new tool for analyzing the underlying structure of FDEs and gaining deeper insights into the interplay between local and non-local dynamics in fractional systems.
基金sponsored by the National Natural Science Foundation of China(Grant No.42141010).
文摘A novel fractional elastoplastic constitutive model is proposed to accurately characterize the deformation of sandstone under true-triaxial stress states.This model is founded on the yield function and the fractional flow rule.The yield function includes parameters that govern the evolution of yield surface,enabling an accurate description of three-dimensional stress states.The direction of plastic flow is governed by the two different fractional orders,which are functions of the plastic internal variable.Additionally,a detailed process is proposed for identifying the yield function parameters and fractional orders.Subsequently,the relationship between the fractional order and the direction of plastic flow in the meridian and deviatoric planes is examined,characterized by the dilation angle and the plastic deflection angle,respectively.The non-orthogonal flow rule,also referred to as the fractional flow rule,allows for a border range of plastic deflection and dilation angles compared to the orthogonal flow rule,thereby significantly enhancing its applicability.The validity and accuracy of proposed model are verified by comparing the analytical solution of the constitutive model with the experimental data.A comparison between the non-orthogonal flow rule and orthogonal flow rule is conducted in both the deviatoric and meridian planes.The further comparison of the stress-strain curves for the non-orthogonal and orthogonal flow rules demonstrates the superiority of the fractional constitutive model.
文摘This study introduces a novel mathematical model to describe the progression of cholera by integrating fractional derivatives with both singular and non-singular kernels alongside stochastic differential equations over four distinct time intervals.The model incorporates three key fractional derivatives:the Caputo-Fabrizio fractional derivative with a non-singular kernel,the Caputo proportional constant fractional derivative with a singular kernel,and the Atangana-Baleanu fractional derivative with a non-singular kernel.We analyze the stability of the core model and apply various numerical methods to approximate the proposed crossover model.To achieve this,the approximation of Caputo proportional constant fractional derivative with Grünwald-Letnikov nonstandard finite difference method is used for the deterministic model with a singular kernel,while the Toufik-Atangana method is employed for models involving a non-singular Mittag-Leffler kernel.Additionally,the integral Caputo-Fabrizio approximation and a two-step Lagrange polynomial are utilized to approximate the model with a non-singular exponential decay kernel.For the stochastic component,the Milstein method is implemented to approximate the stochastic differential equations.The stability and effectiveness of the proposed model and methodologies are validated through numerical simulations and comparisons with real-world cholera data from Yemen.The results confirm the reliability and practical applicability of the model,providing strong theoretical and empirical support for the approach.
文摘We propose a fractional-order improved Fitz Hugh–Nagumo(FHN)neuron model in terms of a generalized Caputo fractional derivative.Following the existence of a unique solution for the proposed model,we derive the numerical solution using a recently proposed L1 predictor–corrector method.The given method is based on the L1-type discretization algorithm and the spline interpolation scheme.We perform the error and stability analyses for the given method.We perform graphical simulations demonstrating that the proposed FHN neuron model generates rich electrical activities of periodic spiking patterns,chaotic patterns,and quasi-periodic patterns.The motivation behind proposing a fractional-order improved FHN neuron model is that such a system can provide a more nuanced description of the process with better understanding and simulation of the neuronal responses by incorporating memory effects and non-local dynamics,which are inherent to many biological systems.
基金supported via funding from Prince Sattam bin Abdulaziz University project number(PSAU/2024/R/1445).
文摘Being a nonlinear operator,fractional derivatives can affect the enforcement of existence at any given time.As a result,the memory effect has an impact on all nonlinear processes modeled by fractional order differential equations(FODEs).The goal of this study is to increase the fractional model of the TB virus’s(FMTBV)accuracy.Stochastic solvers have never been used to solve FMTBV previously.The Bayesian regularized artificial(BRA)method and neural networks(NNs),often referred to as BRA-NNs,were used to solve the FMTBV model.Each scenario features five occurrences that each reflect a different order of derivatives,ranging from 0.8,0.85,0.9,0.95,and 1,as well as five potential rates for different parameters.Training data made up 90%of the data,testing data made up 5%,and validation data made up 5%of the data used to illustrate the FMTBV’s approximations.To verify that the BRA-NNs were correct,the generated simulations were described in the following solutions using the FOLotkaVolterra approach in MATLAB.Comprehensive Simulink results in terms of mean square error,error histogram,and regression analysis investigations further highlight the competence,dependability,and accuracy of the suggested BRA-NNs.
基金supported by the Fundacao para a Ciencia e Tecnologia,FCT,under the project https://doi.org/10.54499/UIDB/04674/2020(accessed on 1 January 2025).
文摘In 2022,Leukemia is the 13th most common diagnosis of cancer globally as per the source of the International Agency for Research on Cancer(IARC).Leukemia is still a threat and challenge for all regions because of 46.6%infection in Asia,and 22.1%and 14.7%infection rates in Europe and North America,respectively.To study the dynamics of Leukemia,the population of cells has been divided into three subpopulations of cells susceptible cells,infected cells,and immune cells.To investigate the memory effects and uncertainty in disease progression,leukemia modeling is developed using stochastic fractional delay differential equations(SFDDEs).The feasible properties of positivity,boundedness,and equilibria(i.e.,Leukemia Free Equilibrium(LFE)and Leukemia Present Equilibrium(LPE))of the model were studied rigorously.The local and global stabilities and sensitivity of the parameters around the equilibria under the assumption of reproduction numbers were investigated.To support the theoretical analysis of the model,the Grunwald Letnikov Nonstandard Finite Difference(GL-NSFD)method was used to simulate the results of each subpopulation with memory effect.Also,the positivity and boundedness of the proposed method were studied.Our results show how different methods can help control the cell population and give useful advice to decision-makers on ways to lower leukemia rates in communities.
基金the financial support from the National Natural Science Foundation of China(No.52109119)the Guangxi Natural Science Foundation(No.2021GXNSFBA075030)+2 种基金the Guangxi Science and Technology Project(No.Guike AD20325002)the Chinese Postdoctoral Science Fund Project(No.2022 M723408)the Open Research Fund of State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin(China Institute of Water Resources and Hydropower Research)(No.IWHR-SKL-202202).
文摘Mechanical excavation,blasting,adjacent rockburst and fracture slip that occur during mining excavation impose dynamic loads on the rock mass,leading to further fracture of damaged surrounding rock in three-dimensional high-stress and even causing disasters.Therefore,a novel complex true triaxial static-dynamic combined loading method reflecting underground excavation damage and then frequent intermittent disturbance failure is proposed.True triaxial static compression and intermittent disturbance tests are carried out on monzogabbro.The effects of intermediate principal stress and amplitude on the strength characteristics,deformation characteristics,failure characteristics,and precursors of monzogabbro are analyzed,intermediate principal stress and amplitude increase monzogabbro strength and tensile fracture mechanism.Rapid increases in microseismic parameters during rock loading can be precursors for intermittent rock disturbance.Based on the experimental result,the new damage fractional elements and method with considering crack initiation stress and crack unstable stress as initiation and acceleration condition of intermittent disturbance irreversible deformation are proposed.A novel three-dimensional disturbance fractional deterioration model considering the intermediate principal stress effect and intermittent disturbance damage effect is established,and the model predicted results align well with the experimental results.The sensitivity of stress states and model parameters is further explored,and the intermittent disturbance behaviors at different f are predicted.This study provides valuable theoretical bases for the stability analysis of deep mining engineering under dynamic loads.
基金support from the National Science Foundation of China(22078190)the National Key R&D Plan of China(2020YFB1505802).
文摘Joint time–frequency analysis is an emerging method for interpreting the underlying physics in fuel cells,batteries,and supercapacitors.To increase the reliability of time–frequency analysis,a theoretical correlation between frequency-domain stationary analysis and time-domain transient analysis is urgently required.The present work formularizes a thorough model reduction of fractional impedance spectra for electrochemical energy devices involving not only the model reduction from fractional-order models to integer-order models and from high-to low-order RC circuits but also insight into the evolution of the characteristic time constants during the whole reduction process.The following work has been carried out:(i)the model-reduction theory is addressed for typical Warburg elements and RC circuits based on the continued fraction expansion theory and the response error minimization technique,respectively;(ii)the order effect on the model reduction of typical Warburg elements is quantitatively evaluated by time–frequency analysis;(iii)the results of time–frequency analysis are confirmed to be useful to determine the reduction order in terms of the kinetic information needed to be captured;and(iv)the results of time–frequency analysis are validated for the model reduction of fractional impedance spectra for lithium-ion batteries,supercapacitors,and solid oxide fuel cells.In turn,the numerical validation has demonstrated the powerful function of the joint time–frequency analysis.The thorough model reduction of fractional impedance spectra addressed in the present work not only clarifies the relationship between time-domain transient analysis and frequency-domain stationary analysis but also enhances the reliability of the joint time–frequency analysis for electrochemical energy devices.
基金Supported by Shanghai Artificial Intelligence Laboratory。
文摘This paper develops an Ito-type fractional pathwise integration theory for fractional Brownian motion with Hurst parameters H∈(1/3,1/2],using the Lyons'rough path framework.This approach is designed to fill gaps in conventional stochastic calculus models that fail to account for temporal persistence prevalent in dynamic systems such as those found in economics,finance,and engineering.The pathwise-defined method not only meets the zero expectation criterion but also addresses the challenges of integrating non-semimartingale processes,which traditional Ito calculus cannot handle.We apply this theory to fractional Black–Scholes models and high-dimensional fractional Ornstein–Uhlenbeck processes,illustrating the advantages of this approach.Additionally,the paper discusses the generalization of It?integrals to rough differential equations(RDE)driven by f BM,emphasizing the necessity of integrand-specific adaptations in the It?rough path lift for stochastic modeling.
基金Project(2024JJ2074) supported by the Natural Science Foundation of Hunan Province,ChinaProject(22376221) supported by the National Natural Science Foundation of ChinaProject(2023QNRC001) supported by the Young Elite Scientists Sponsorship Program by CAST,China。
文摘Driven by rapid technological advancements and economic growth,mineral extraction and metal refining have increased dramatically,generating huge volumes of tailings and mine waste(TMWs).Investigating the morphological fractions of heavy metals and metalloids(HMMs)in TMWs is key to evaluating their leaching potential into the environment;however,traditional experiments are time-consuming and labor-intensive.In this study,10 machine learning(ML)algorithms were used and compared for rapidly predicting the morphological fractions of HMMs in TMWs.A dataset comprising 2376 data points was used,with mineral composition,elemental properties,and total concentration used as inputs and concentration of morphological fraction used as output.After grid search optimization,the extra tree model performed the best,achieving coefficient of determination(R2)of 0.946 and 0.942 on the validation and test sets,respectively.Electronegativity was found to have the greatest impact on the morphological fraction.The models’performance was enhanced by applying an ensemble method to the top three optimal ML models,including gradient boosting decision tree,extra trees and categorical boosting.Overall,the proposed framework can accurately predict the concentrations of different morphological fractions of HMMs in TMWs.This approach can minimize detection time,aid in the safe management and recovery of TMWs.
文摘Polydeoxyribonucleotide(PDRN)has been utilized in clinical practice for an extended period;however,its application in the cosmetics is relatively recent.This study aims to explore the research progress of PDRN regarding its skin repair and anti-aging properties.To evaluate the potential skin repair,soothing,anti-wrinkle and firming effects of PDRN essence via both in vitro and in vivo test method.This study employed in vitro and in vivo test to assess the skin repair and anti-wrinkle effects.The 3D skin model(FulKutis®)was utilized to verify the effects of the PDRN essence on anti-inflammation,barrier repair,and anti-aging.In human test,a randomized,half-face comparison test with PDRN essence and the placebo was conducted with 33 Chinese subjects who met the test criteria.During the test,the skin conditions in terms of the a*value,facial red area ratio,and Transepidermal Water Loss(TEWL)were evaluated at 30 min,4 h,1 day,and 3 days;the skin conditions in terms of skin elasticity and firmness,skin wrinkles were evaluated at 42 days.Subjects’self-assessments were collected at 3 days and 42 days.The FulKutis■experiments demonstrated that the PDRN essence significantly decreased the levels of IL-1α,TNF-α,and PGE2,and improved the protein levels of Filaggrin,Loricrin,Collagen I,Collagen IV,and the thickness of the epidermal living cell layer.In the human study,the a*value,red area ratio,TEWL,and skin-related parameters(R2,R5,R7,F4,and skin wrinkles)on the test face side exhibited greater improvement compared to the control face side with statistically significant differences.Additionally,subject selfassessments revealed high satisfaction with the PDRN essence.The PDRN essence applied after non-ablative fractional laser treatment promotes barrier repair and soothing effects,shortens the recovery period,and enhances facial firmness and wrinkle improvement at the crow’s feet and undereye regions.No adverse events related to the tested cosmetics were observed.
基金funded by the Third Xinjiang Comprehensive Scientific Investigation Project,China(2022xjkk0702)the Western Young Scholars Project of the Chinese Academy of Sciences(2022-XBQNXZ-001)the Tianshan Talent Development Program,China(2022TSYCCX0006).
文摘The rapid acceleration of global warming and intensifying human activities have exacerbated the fragility and climate sensitivity of ecosystems worldwide,particularly in arid regions.Vegetation,a key component of ecosystems,is critical in enhancing the ecological environment.The Ertix River Basin(ERB)is a transboundary watershed that spans multiple countries,mostly in arid regions.However,research on the fractional vegetation coverage(FVC)and its driving factors in the ERB remains limited.Investigating the spatiotemporal changes in the FVC and its relationship with various factors in the ERB can offer scientific support for optimizing regional vegetation restoration policies and promoting the coordinated development of human-environment interactions.The Moderate-resolution Imaging Spectroradiometer(MODIS)MYD13Q1 V6 data were obtained via the Google Earth Engine platform,and methods including the pixel dichotomy method,Theil-Sen median trend analysis,and Mann‒Kendall test were employed to examine the spatiotemporal dynamics of the FVC in the ERB from 2003 to 2023,with future trend forecast using the Hurst index.The impacts of natural and socioeconomic factors on the FVC were evaluated through the partial least squares-structural equation model(PLS-SEM).The results indicated that the FVC in the ERB showed a slight degradation trend with an average annual decrease of 0.046%during 2003-2023,with significant changes occurring in 2004,2010,and 2019.Spatially,53.380%of the study area was degraded,and the change in the FVC increased gradually from southeast to northwest.The FVC in 63.000%of the study area was highly stable and displayed long-term persistence;and the direct impact of natural factors(path coefficient of 0.617)on the FVC was significantly higher than that of socioeconomic factors(0.167).Among the natural factors,precipitation(0.999)was the most significant.This study reveals the significant impacts of natural and socioeconomic factors on vegetation dynamics in arid regions,and provides a scientific basis for transnational ecological conservation.
文摘In this study,a numerical method based on the Pell-Lucas polynomials(PLPs)is developed to solve the fractional order HIV/AIDS epidemic model with a treatment compartment.The HIV/AIDS mathematical model with a treatment compartment is divided into five classes,namely,susceptible patients(S),HIV-positive individuals(I),individuals with full-blown AIDS but not receiving ARV treatment(A),individuals being treated(T),and individuals who have changed their sexual habits sufficiently(R).According to the method,by utilizing the PLPs and the collocation points,we convert the fractional order HIV/AIDS epidemic model with a treatment compartment into a nonlinear system of the algebraic equations.Also,the error analysis is presented for the Pell-Lucas approximation method.The aim of this study is to observe the behavior of five populations after 200 days when drug treatment is applied to HIV-infectious and full-blown AIDS people.To demonstrate the usefulness of this method,the applications are made on the numerical example with the help of MATLAB.In addition,four cases of the fractional order derivative(p=1,p=0.95,p=0.9,p=0.85)are examined in the range[0,200].Owing to applications,we figured out that the outcomes have quite decent errors.Also,we understand that the errors decrease when the value of N increases.The figures in this study are created in MATLAB.The outcomes indicate that the presented method is reasonably sufficient and correct.
文摘In this paper, we consider the Cauchy problem of 3-dimensional tropical climate model. This model reflects the interaction and coupling among the barotropic mode u, the first baroclinic mode v of the velocity and the temperature θ. The systems with fractional dissipation studied here may arise in the modeling of geophysical circumstances. Mathematically these systems allow simultaneous examination of a family of systems with various levels of regularization. The aim here is the global strong solution with the least dissipation. By energy estimate and delicate analysis, we prove the existence of global solution under three different cases: first, with the help of damping terms, the global strong solution of the system with Λ<sup>2a</sup>u, Λ<sup>2β</sup>v and Λ<sup>2γ</sup> θ for;and second, the global strong solution of the system for with damping terms;finally, the global strong solution of the system for without any damping terms, which improve the known existence theory for this system.
文摘The outbreak of COVID-19 in 2019 resulted in numerous infections and deaths. In order to better study the transmission of COVID-19, this article adopts an improved fractional-order SIR model. Firstly, the properties of the model are studied, including the feasible domain and bounded solutions of the system. Secondly, the stability of the system is discussed, among other things. Then, the GMMP method is introduced to obtain numerical solutions for the COVID-19 system and combined with the improved MH-NMSS-PSO parameter estimation method to fit the real data of Delhi, India from April 1, 2020 to June 30, 2020. The results show that the fitting effect is quite ideal. Finally, long-term predictions were made on the number of infections. We accurately estimate that the peak number of infections in Delhi, India, can reach around 2.1 million. This paper also compares the fitting performance of the integer-order COVID-19 model and the fractional-order COVID-19 model using the real data from Delhi. The results indicate that the fractional-order model with different orders, as we proposed, performs the best.
文摘This paper investigates an improved SIR model for COVID-19 based on the Caputo fractional derivative. Firstly, the properties of the model are studied, including the feasible domain and bounded solutions of the system. Secondly, the stability of the system is discussed, among other things. Then, the GMMP method is introduced to obtain numerical solutions for the COVID-19 system. Numerical simulations were conducted using MATLAB, and the results indicate that our model is valuable for studying virus transmission.
基金The project supported by the National Natural Science Foundation of China (10002003)Foundation for University Key Teacher by the Ministry of EducationResearch Fund for the Doctoral Program of Higher Education
文摘The fractional calculus approach in the constitutive relationship model of viscoelastic fluid is introduced.The flow near a wall suddenly set in mo- tion is studied for a non-Newtonian viscoelastic fluid with the fractional Maxwell model.Exact solutions of velocity and stress are obtained by using the discrete in- verse Laplace transform of the sequential fractional derivatives.It is found that the effect of the fractional orders in the constitutive relationship on the flow field is signif- icant.The results show that for small times there are appreciable viscoelastic effects on the shear stress at the plate,for large times the viscoelastic effects become weak.
基金financial supports provided by the Fundamental Research Funds (Grant 106112015CDJXY200008)
文摘Many constitutive models exist to characterise the cyclic behaviour of granular soils but can only simulate deformations for very limited cycles. Fractional derivatives have been regarded as one potential instrument for modelling memory-dependent phenomena. In this paper, the physical connection between the fractional derivative order and the fractal dimension of granular soils is investigated in detail. Then a modified elasto-plastic constitutive model is proposed for evaluating the long-term deformation of granular soils under cyclic loading by incorporating the concept of fac- tional calculus. To describe the flow direction of granular soils under cyclic loading, a cyclic flow potential consider- ing particle breakage is used. Test results of several types of granular soils are used to validate the model performance.
