Fractional discrete systems can enable the modeling and control of the complicated processes more adaptable through the concept of versatility by providing systemdynamics’descriptions withmore degrees of freedom.Nume...Fractional discrete systems can enable the modeling and control of the complicated processes more adaptable through the concept of versatility by providing systemdynamics’descriptions withmore degrees of freedom.Numerical approaches have become necessary and sufficient to be addressed and employed for benefiting from the adaptability of such systems for varied applications.A variety of fractional Layla and Majnun model(LMM)system kinds has been proposed in the current work where some of these systems’key behaviors are addressed.In addition,the necessary and sufficient conditions for the stability and asymptotic stability of the fractional dynamic systems are investigated,as a result of which,the necessary requirements of the LMM to achieve constant and asymptotically steady zero resolutions are provided.As a special case,when Layla and Majnun have equal feelings,we propose an analysis of the system in view of its equilibrium and fixed point sets.Considering that the system has marginal stability if its eigenvalues have both negative and zero real portions,it is demonstrated that the system neither converges nor diverges to a steady trajectory or equilibrium point.It,rather,continues to hover along the line separating stability and instability based on the fractional LMM system.展开更多
This article studies the existence and uniqueness of the mild solution of a family of control systems with a delay that are governed by the nonlinear fractional evolution differential equations in Banach spaces.Moreov...This article studies the existence and uniqueness of the mild solution of a family of control systems with a delay that are governed by the nonlinear fractional evolution differential equations in Banach spaces.Moreover,we establish the controllability of the considered system.To do so,first,we investigate the approximate controllability of the corresponding linear system.Subsequently,we prove the nonlinear system is approximately controllable if the corresponding linear system is approximately controllable.To reach the conclusions,the theory of resolvent operators,the Banach contraction mapping principle,and fixed point theorems are used.While concluding,some examples are given to demonstrate the efficacy of the proposed results.展开更多
Background Non-invasive computed tomography angiography(CTA)-based fractional flow reserve(CT-FFR)could become a gatekeeper to invasive coronary angiography.Deep learning(DL)-based CT-FFR has shown promise when compar...Background Non-invasive computed tomography angiography(CTA)-based fractional flow reserve(CT-FFR)could become a gatekeeper to invasive coronary angiography.Deep learning(DL)-based CT-FFR has shown promise when compared to invasive FFR.To evaluate the performance of a DL-based CT-FFR technique,DeepVessel FFR(DVFFR).Methods This retrospective study was designed for iScheMia Assessment based on a Retrospective,single-center Trial of CTFFR(SMART).Patients suspected of stable coronary artery disease(CAD)and undergoing both CTA and invasive FFR examinations were consecutively selected from the Beijing Anzhen Hospital between January 1,2016 to December 30,2018.FFR obtained during invasive coronary angiography was used as the reference standard.DVFFR was calculated blindly using a DL-based CTFFR approach that utilized the complete tree structure of the coronary arteries.Results Three hundred and thirty nine patients(60.5±10.0 years and 209 men)and 414 vessels with direct invasive FFR were included in the analysis.At per-vessel level,sensitivity,specificity,accuracy,positive predictive value(PPV)and negative predictive value(NPV)of DVFFR were 94.7%,88.6%,90.8%,82.7%,and 96.7%,respectively.The area under the receiver operating characteristics curve(AUC)was 0.95 for DVFFR and 0.56 for CTA-based assessment with a significant difference(P<0.0001).At patient level,sensitivity,specificity,accuracy,PPV and NPV of DVFFR were 93.8%,88.0%,90.3%,83.0%,and 95.8%,respectively.The computation for DVFFR was fast with the average time of 22.5±1.9 s.Conclusions The results demonstrate that DVFFR was able to evaluate lesion hemodynamic significance accurately and effectively with improved diagnostic performance over CTA alone.Coronary artery disease(CAD)is a critical disease in which coronary artery luminal narrowing may result in myocardial ischemia.Early and effective assessment of myocardial ischemia is essential for optimal treatment planning so as to improve the quality of life and reduce medical costs.展开更多
In this paper,we present local functional law of the iterated logarithm for Cs?rg?-Révész type increments of fractional Brownian motion.The results obtained extend works of Gantert[Ann.Probab.,1993,21(2):104...In this paper,we present local functional law of the iterated logarithm for Cs?rg?-Révész type increments of fractional Brownian motion.The results obtained extend works of Gantert[Ann.Probab.,1993,21(2):1045-1049]and Monrad and Rootzén[Probab.Theory Related Fields,1995,101(2):173-192].展开更多
Core power is a key parameter of nuclear reactor.Traditionally,the proportional-integralderivative(PID)controllers are used to control the core power.Fractional-order PID(FOPID)controller represents the cutting edge i...Core power is a key parameter of nuclear reactor.Traditionally,the proportional-integralderivative(PID)controllers are used to control the core power.Fractional-order PID(FOPID)controller represents the cutting edge in core power control research.In comparing with the integer-order models,fractional-order models describe the variation of core power more accurately,thus provide a comprehensive and realistic depiction for the power and state changes of reactor core.However,current fractional-order controllers cannot adjust their parameters dynamically to response the environmental changes or demands.In this paper,we aim at the stable control and dynamic responsiveness of core power.Based on the strong selflearning ability of artificial neural network(ANN),we propose a composite controller combining the ANN and FOPID controller.The FOPID controller is firstly designed and a back propagation neural network(BPNN)is then utilized to optimize the parameters of FOPID.It is shown by simulation that the composite controller enables the real-time parameter tuning via ANN and retains the advantage of FOPID controller.展开更多
In this paper,we study the existence of least energy solutions for the following nonlinear fractional Schrodinger–Poisson system{(−∆)^(s)u+V(x)u+φu=f(u)in R^(3),(−∆)^(t)φ=u^(2)in R^(3),where s∈(3/4,1),t∈(0,1).Und...In this paper,we study the existence of least energy solutions for the following nonlinear fractional Schrodinger–Poisson system{(−∆)^(s)u+V(x)u+φu=f(u)in R^(3),(−∆)^(t)φ=u^(2)in R^(3),where s∈(3/4,1),t∈(0,1).Under some assumptions on V(x)and f,using Nehari–Pohozaev identity and the arguments of Brezis–Nirenberg,the monotonic trick and global compactness lemma,we prove the existence of a nontrivial least energy solution.展开更多
In this paper,we prove the transportation cost-information inequalities on the space of continuous paths with respect to the L~2-metric and the uniform metric for the law of the mild solution to the stochastic heat eq...In this paper,we prove the transportation cost-information inequalities on the space of continuous paths with respect to the L~2-metric and the uniform metric for the law of the mild solution to the stochastic heat equation defined on[0,T]×[0,1]driven by double-parameter fractional noise.展开更多
This study investigates the dynamics of pneumococcal pneumonia using a novel fractal-fractional Susceptible-Carrier-Infected-Recovered model formulated with the Atangana-Baleanu in Caputo(ABC)sense.Unlike traditional ...This study investigates the dynamics of pneumococcal pneumonia using a novel fractal-fractional Susceptible-Carrier-Infected-Recovered model formulated with the Atangana-Baleanu in Caputo(ABC)sense.Unlike traditional epidemiological models that rely on classical or Caputo fractional derivatives,the proposed model incorporates nonlocal memory effects,hereditary properties,and complex transmission dynamics through fractalfractional calculus.The Atangana-Baleanu operator,with its non-singular Mittag-Leffler kernel,ensures a more realistic representation of disease progression compared to classical integer-order models and singular kernel-based fractional models.The study establishes the existence and uniqueness of the proposed system and conducts a comprehensive stability analysis,including local and global stability.Furthermore,numerical simulations illustrate the effectiveness of the ABC operator in capturing long-memory effects and nonlocal interactions in disease transmission.The results provide valuable insights into public health interventions,particularly in optimizing vaccination strategies,treatment approaches,and mitigation measures.By extending epidemiological modeling through fractal-fractional derivatives,this study offers an advanced framework for analyzing infectious disease dynamics with enhanced accuracy and predictive capabilities.展开更多
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
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
By using the Ljusternik-Schnirelmann category and variational method,we s-tudy the existence,multiplicity and concentration of solutions to the fractional Schrodinger equation with potentials competition as follows,ε...By using the Ljusternik-Schnirelmann category and variational method,we s-tudy the existence,multiplicity and concentration of solutions to the fractional Schrodinger equation with potentials competition as follows,ε^(N)(-△)^(s)N/sμ+V(x)|μ|^(N/s-2μ)=Q(x)h(μ)in R^(N),where ε>0 is a parameter,s ∈(0,1),2≤p<+oo and N=ps.The nonlinear term h is a diferentiable function with exponential critical growth,the absorption potential V and the reaction potential Q are continuous functions.展开更多
Fractional-N phase-locked loops(PLLs)are widely deployed in high-speed communication systems to generate local oscillator(LO)or clock signals with precise frequency.To support sophisticated modulations for increasing ...Fractional-N phase-locked loops(PLLs)are widely deployed in high-speed communication systems to generate local oscillator(LO)or clock signals with precise frequency.To support sophisticated modulations for increasing the data rate,the PLL needs to generate low-jitter output[1].展开更多
In this paper, we study the stability of a class of conformable fractional-order systems using the Lyapunov function. We assume that the nonlinear part of the system satisfies the one-sided Lipschitz condition and the...In this paper, we study the stability of a class of conformable fractional-order systems using the Lyapunov function. We assume that the nonlinear part of the system satisfies the one-sided Lipschitz condition and the quadratic inner-bounded condition. We provide some sufficient conditions that ensure the asymptotic stability of the system. Furthermore, we present the construction of a feedback stabilizing controller for conformable fractional bilinear systems.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
The air spring is a non-metallic spring device that utilizes the deformation of flexible materials and the compression of air to generate restoring force, achieving vibration damping and buffering effects. It features...The air spring is a non-metallic spring device that utilizes the deformation of flexible materials and the compression of air to generate restoring force, achieving vibration damping and buffering effects. It features height adjustment and highfrequency vibration isolation. Air springs exhibit significant viscoelastic and memory characteristics. Traditional dynamic models of air springs are complex and unable to accurately describe their viscoelastic properties. This paper introduces fractional calculus theory to study them. Through experimental research on air springs, test data are analyzed to obtain their mechanical properties under different working conditions. A fractional-order nonlinear dynamic model of the air spring is established, and the model parameters are identified using the least squares method. The experimental data are fitted to verify the model's accuracy.展开更多
This paper focuses on applying the barycentric Lagrange interpolation collocation method(BLICM)for solving 2D time-fractional diffusion-wave equation(TFDWE).In order to obtain the discrete format of the equation,we co...This paper focuses on applying the barycentric Lagrange interpolation collocation method(BLICM)for solving 2D time-fractional diffusion-wave equation(TFDWE).In order to obtain the discrete format of the equation,we construct the multivariate barycentric Lagrange interpolation approximation function and process the integral terms by using the Gauss-Legendre quadrature formula.We provide a detailed error analysis of the discrete format on the second kind of Chebyshev nodes.The efficacy of the proposed method is substantiated by some numerical experiments.The results of these experiments demonstrate that our method can obtain high-precision numerical solutions for fractional partial differential equations.Additionally,the method's capability to achieve high precision with a reduced number of nodes is confirmed.展开更多
The Rössler attractor model is an important model that provides valuable insights into the behavior of chaotic systems in real life and is applicable in understanding weather patterns,biological systems,and secur...The Rössler attractor model is an important model that provides valuable insights into the behavior of chaotic systems in real life and is applicable in understanding weather patterns,biological systems,and secure communications.So,this work aims to present the numerical performances of the nonlinear fractional Rössler attractor system under Caputo derivatives by designing the numerical framework based on Ultraspherical wavelets.The Caputo fractional Rössler attractor model is simulated into two categories,(i)Asymmetric and(ii)Symmetric.The Ultraspherical wavelets basis with suitable collocation grids is implemented for comprehensive error analysis in the solutions of the Caputo fractional Rössler attractor model,depicting each computation in graphs and tables to analyze how fractional order affects the model’s dynamics.Approximate solutions obtained through the proposed scheme for integer order are well comparable with the fourth-order Runge-Kutta method.Also,the stability analyses of the considered model are discussed for different equilibrium points.Various fractional orders are considered while performing numerical simulations for the Caputo fractional Rössler attractor model by using Mathematica.The suggested approach can solve another non-linear fractional model due to its straightforward implementation.展开更多
In this article,several kinds of novel exact waves solutions of three well-known different space-time fractional nonlinear coupled waves dynamical models are constructed with the aid of simpler and effective improved ...In this article,several kinds of novel exact waves solutions of three well-known different space-time fractional nonlinear coupled waves dynamical models are constructed with the aid of simpler and effective improved auxiliary equation method.Firstly we will investigate space-time fractional coupled Boussinesq-Burger dynamical model,which is used to model the propagation of water waves in shallow sea and harbor,and has many applications in ocean engineering.Secondly,we will investigate the space-time fractional coupled Drinfeld-SokolovWilson equation which is used to characterize the nonlinear surface gravity waves propagation over horizontal seabed.Thirdly,we will investigate the space-time-space fractional coupled Whitham-Broer-Kaup equation which is used to model the shallow water waves in a porous medium near a dam.We obtained different solutions in terms of trigonometric,hyperbolic,exponential and Jacobi elliptic functions.Furthermore,graphics are plotted to explain the different novel structures of obtained solutions such as multi solitons interaction,periodic soliton,bright and dark solitons,Kink and anti-Kink solitons,breather-type waves and so on,which have applications in ocean engineering,fluid mechanics and other related fields.We hope that our results obtained in this article will be useful to understand many novel physical phenomena in applied sciences and other related fields.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
This paper addresses the evolution problem governed by the fractional sweeping process with prox-regular nonconvex constraints.The values of the moving set are time and state-dependent.The aim is to illustrate how a f...This paper addresses the evolution problem governed by the fractional sweeping process with prox-regular nonconvex constraints.The values of the moving set are time and state-dependent.The aim is to illustrate how a fixed point method can establish an existence theorem for this fractional nonlinear evolution problem.By combining Schauder’s fixed point theorem with a well-posedness theorem when the set C is independent of the state u(i.e.C:=C(t),as presented in[22,23]),we prove the existence of a solution to our quasi-variational fractional sweeping process in infinite-dimensional Hilbert spaces.Similar to the conventional state-dependent sweeping process,achieving this result requires a condition on the size of the Lipschitz constant of the moving set relative to the state.展开更多
基金supported by Ajman University Internal Research Grant No.(DRGS Ref.2024-IRGHBS-3).
文摘Fractional discrete systems can enable the modeling and control of the complicated processes more adaptable through the concept of versatility by providing systemdynamics’descriptions withmore degrees of freedom.Numerical approaches have become necessary and sufficient to be addressed and employed for benefiting from the adaptability of such systems for varied applications.A variety of fractional Layla and Majnun model(LMM)system kinds has been proposed in the current work where some of these systems’key behaviors are addressed.In addition,the necessary and sufficient conditions for the stability and asymptotic stability of the fractional dynamic systems are investigated,as a result of which,the necessary requirements of the LMM to achieve constant and asymptotically steady zero resolutions are provided.As a special case,when Layla and Majnun have equal feelings,we propose an analysis of the system in view of its equilibrium and fixed point sets.Considering that the system has marginal stability if its eigenvalues have both negative and zero real portions,it is demonstrated that the system neither converges nor diverges to a steady trajectory or equilibrium point.It,rather,continues to hover along the line separating stability and instability based on the fractional LMM system.
文摘This article studies the existence and uniqueness of the mild solution of a family of control systems with a delay that are governed by the nonlinear fractional evolution differential equations in Banach spaces.Moreover,we establish the controllability of the considered system.To do so,first,we investigate the approximate controllability of the corresponding linear system.Subsequently,we prove the nonlinear system is approximately controllable if the corresponding linear system is approximately controllable.To reach the conclusions,the theory of resolvent operators,the Banach contraction mapping principle,and fixed point theorems are used.While concluding,some examples are given to demonstrate the efficacy of the proposed results.
文摘Background Non-invasive computed tomography angiography(CTA)-based fractional flow reserve(CT-FFR)could become a gatekeeper to invasive coronary angiography.Deep learning(DL)-based CT-FFR has shown promise when compared to invasive FFR.To evaluate the performance of a DL-based CT-FFR technique,DeepVessel FFR(DVFFR).Methods This retrospective study was designed for iScheMia Assessment based on a Retrospective,single-center Trial of CTFFR(SMART).Patients suspected of stable coronary artery disease(CAD)and undergoing both CTA and invasive FFR examinations were consecutively selected from the Beijing Anzhen Hospital between January 1,2016 to December 30,2018.FFR obtained during invasive coronary angiography was used as the reference standard.DVFFR was calculated blindly using a DL-based CTFFR approach that utilized the complete tree structure of the coronary arteries.Results Three hundred and thirty nine patients(60.5±10.0 years and 209 men)and 414 vessels with direct invasive FFR were included in the analysis.At per-vessel level,sensitivity,specificity,accuracy,positive predictive value(PPV)and negative predictive value(NPV)of DVFFR were 94.7%,88.6%,90.8%,82.7%,and 96.7%,respectively.The area under the receiver operating characteristics curve(AUC)was 0.95 for DVFFR and 0.56 for CTA-based assessment with a significant difference(P<0.0001).At patient level,sensitivity,specificity,accuracy,PPV and NPV of DVFFR were 93.8%,88.0%,90.3%,83.0%,and 95.8%,respectively.The computation for DVFFR was fast with the average time of 22.5±1.9 s.Conclusions The results demonstrate that DVFFR was able to evaluate lesion hemodynamic significance accurately and effectively with improved diagnostic performance over CTA alone.Coronary artery disease(CAD)is a critical disease in which coronary artery luminal narrowing may result in myocardial ischemia.Early and effective assessment of myocardial ischemia is essential for optimal treatment planning so as to improve the quality of life and reduce medical costs.
基金Supported by NSFC(Nos.11661025,12161024)Natural Science Foundation of Guangxi(Nos.2020GXNSFAA159118,2021GXNSFAA196045)+2 种基金Guangxi Science and Technology Project(No.Guike AD20297006)Training Program for 1000 Young and Middle-aged Cadre Teachers in Universities of GuangxiNational College Student's Innovation and Entrepreneurship Training Program(No.202110595049)。
文摘In this paper,we present local functional law of the iterated logarithm for Cs?rg?-Révész type increments of fractional Brownian motion.The results obtained extend works of Gantert[Ann.Probab.,1993,21(2):1045-1049]and Monrad and Rootzén[Probab.Theory Related Fields,1995,101(2):173-192].
文摘Core power is a key parameter of nuclear reactor.Traditionally,the proportional-integralderivative(PID)controllers are used to control the core power.Fractional-order PID(FOPID)controller represents the cutting edge in core power control research.In comparing with the integer-order models,fractional-order models describe the variation of core power more accurately,thus provide a comprehensive and realistic depiction for the power and state changes of reactor core.However,current fractional-order controllers cannot adjust their parameters dynamically to response the environmental changes or demands.In this paper,we aim at the stable control and dynamic responsiveness of core power.Based on the strong selflearning ability of artificial neural network(ANN),we propose a composite controller combining the ANN and FOPID controller.The FOPID controller is firstly designed and a back propagation neural network(BPNN)is then utilized to optimize the parameters of FOPID.It is shown by simulation that the composite controller enables the real-time parameter tuning via ANN and retains the advantage of FOPID controller.
基金Supported by NSFC(No.12561023)partly by the Provincial Natural Science Foundation of Jiangxi,China(Nos.20232BAB201001,20202BAB211004)。
文摘In this paper,we study the existence of least energy solutions for the following nonlinear fractional Schrodinger–Poisson system{(−∆)^(s)u+V(x)u+φu=f(u)in R^(3),(−∆)^(t)φ=u^(2)in R^(3),where s∈(3/4,1),t∈(0,1).Under some assumptions on V(x)and f,using Nehari–Pohozaev identity and the arguments of Brezis–Nirenberg,the monotonic trick and global compactness lemma,we prove the existence of a nontrivial least energy solution.
基金Partially supported by Postgraduate Research and Practice Innovation Program of Jiangsu Province(Nos.KYCX22-2211,KYCX22-2205)。
文摘In this paper,we prove the transportation cost-information inequalities on the space of continuous paths with respect to the L~2-metric and the uniform metric for the law of the mild solution to the stochastic heat equation defined on[0,T]×[0,1]driven by double-parameter fractional noise.
基金funded by the Research,Development,and Innovation Authority(RDIA)-Kingdom of Saudi Arabia-with grant number 12803-baha-2023-BU-R-3-1-EI.
文摘This study investigates the dynamics of pneumococcal pneumonia using a novel fractal-fractional Susceptible-Carrier-Infected-Recovered model formulated with the Atangana-Baleanu in Caputo(ABC)sense.Unlike traditional epidemiological models that rely on classical or Caputo fractional derivatives,the proposed model incorporates nonlocal memory effects,hereditary properties,and complex transmission dynamics through fractalfractional calculus.The Atangana-Baleanu operator,with its non-singular Mittag-Leffler kernel,ensures a more realistic representation of disease progression compared to classical integer-order models and singular kernel-based fractional models.The study establishes the existence and uniqueness of the proposed system and conducts a comprehensive stability analysis,including local and global stability.Furthermore,numerical simulations illustrate the effectiveness of the ABC operator in capturing long-memory effects and nonlocal interactions in disease transmission.The results provide valuable insights into public health interventions,particularly in optimizing vaccination strategies,treatment approaches,and mitigation measures.By extending epidemiological modeling through fractal-fractional derivatives,this study offers an advanced framework for analyzing infectious disease dynamics with enhanced accuracy and predictive capabilities.
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.
基金supported by National Natural Science Foundation of China(No.12171152)。
文摘By using the Ljusternik-Schnirelmann category and variational method,we s-tudy the existence,multiplicity and concentration of solutions to the fractional Schrodinger equation with potentials competition as follows,ε^(N)(-△)^(s)N/sμ+V(x)|μ|^(N/s-2μ)=Q(x)h(μ)in R^(N),where ε>0 is a parameter,s ∈(0,1),2≤p<+oo and N=ps.The nonlinear term h is a diferentiable function with exponential critical growth,the absorption potential V and the reaction potential Q are continuous functions.
基金supported by the University of Macao Research Fund under Grant MYRG-GRG2024-00298-IMEby the Macao Science and Technology Development Fund(FDCT)under Grant 0103/2022/AFJ.
文摘Fractional-N phase-locked loops(PLLs)are widely deployed in high-speed communication systems to generate local oscillator(LO)or clock signals with precise frequency.To support sophisticated modulations for increasing the data rate,the PLL needs to generate low-jitter output[1].
文摘In this paper, we study the stability of a class of conformable fractional-order systems using the Lyapunov function. We assume that the nonlinear part of the system satisfies the one-sided Lipschitz condition and the quadratic inner-bounded condition. We provide some sufficient conditions that ensure the asymptotic stability of the system. Furthermore, we present the construction of a feedback stabilizing controller for conformable fractional bilinear systems.
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Project supported by the National Natural Science Foundation of China (Grant Nos. 12072206 and U1934201)Science and Technology Project of Hebei Education Department of Hebei Province, China (Grant No. QN2024254)。
文摘The air spring is a non-metallic spring device that utilizes the deformation of flexible materials and the compression of air to generate restoring force, achieving vibration damping and buffering effects. It features height adjustment and highfrequency vibration isolation. Air springs exhibit significant viscoelastic and memory characteristics. Traditional dynamic models of air springs are complex and unable to accurately describe their viscoelastic properties. This paper introduces fractional calculus theory to study them. Through experimental research on air springs, test data are analyzed to obtain their mechanical properties under different working conditions. A fractional-order nonlinear dynamic model of the air spring is established, and the model parameters are identified using the least squares method. The experimental data are fitted to verify the model's accuracy.
基金Supported by the Scientific Research Foundation for Talents Introduced of Guizhou University of Finance and Economics(Grant No.2023YJ16)the Institute of Complexity Science,Henan University of Technology(Grant No.CSKFJJ-2025-33)the International Science and Technology Cooperation Project of Henan Province(Grant No.252102520007).
文摘This paper focuses on applying the barycentric Lagrange interpolation collocation method(BLICM)for solving 2D time-fractional diffusion-wave equation(TFDWE).In order to obtain the discrete format of the equation,we construct the multivariate barycentric Lagrange interpolation approximation function and process the integral terms by using the Gauss-Legendre quadrature formula.We provide a detailed error analysis of the discrete format on the second kind of Chebyshev nodes.The efficacy of the proposed method is substantiated by some numerical experiments.The results of these experiments demonstrate that our method can obtain high-precision numerical solutions for fractional partial differential equations.Additionally,the method's capability to achieve high precision with a reduced number of nodes is confirmed.
基金"La derivada fraccional generalizada,nuevos resultados y aplicaciones a desigualdades integrales"Cod UIO-077-2024supported via funding from Prince Sattam bin Abdulaziz University project number(PSAU/2025/R/1446).
文摘The Rössler attractor model is an important model that provides valuable insights into the behavior of chaotic systems in real life and is applicable in understanding weather patterns,biological systems,and secure communications.So,this work aims to present the numerical performances of the nonlinear fractional Rössler attractor system under Caputo derivatives by designing the numerical framework based on Ultraspherical wavelets.The Caputo fractional Rössler attractor model is simulated into two categories,(i)Asymmetric and(ii)Symmetric.The Ultraspherical wavelets basis with suitable collocation grids is implemented for comprehensive error analysis in the solutions of the Caputo fractional Rössler attractor model,depicting each computation in graphs and tables to analyze how fractional order affects the model’s dynamics.Approximate solutions obtained through the proposed scheme for integer order are well comparable with the fourth-order Runge-Kutta method.Also,the stability analyses of the considered model are discussed for different equilibrium points.Various fractional orders are considered while performing numerical simulations for the Caputo fractional Rössler attractor model by using Mathematica.The suggested approach can solve another non-linear fractional model due to its straightforward implementation.
文摘In this article,several kinds of novel exact waves solutions of three well-known different space-time fractional nonlinear coupled waves dynamical models are constructed with the aid of simpler and effective improved auxiliary equation method.Firstly we will investigate space-time fractional coupled Boussinesq-Burger dynamical model,which is used to model the propagation of water waves in shallow sea and harbor,and has many applications in ocean engineering.Secondly,we will investigate the space-time fractional coupled Drinfeld-SokolovWilson equation which is used to characterize the nonlinear surface gravity waves propagation over horizontal seabed.Thirdly,we will investigate the space-time-space fractional coupled Whitham-Broer-Kaup equation which is used to model the shallow water waves in a porous medium near a dam.We obtained different solutions in terms of trigonometric,hyperbolic,exponential and Jacobi elliptic functions.Furthermore,graphics are plotted to explain the different novel structures of obtained solutions such as multi solitons interaction,periodic soliton,bright and dark solitons,Kink and anti-Kink solitons,breather-type waves and so on,which have applications in ocean engineering,fluid mechanics and other related fields.We hope that our results obtained in this article will be useful to understand many novel physical phenomena in applied sciences and other related fields.
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 by the Natural Science Foundation of Guangxi(2021GXNSFFA196004,2024GXNSFBA010337)the NNSF of China(12371312)+1 种基金the Natural Science Foundation of Chongqing(CSTB2024NSCQ-JQX0033)supported by the project cooperation between Guangxi Normal University and Yulin Normal University.
文摘This paper addresses the evolution problem governed by the fractional sweeping process with prox-regular nonconvex constraints.The values of the moving set are time and state-dependent.The aim is to illustrate how a fixed point method can establish an existence theorem for this fractional nonlinear evolution problem.By combining Schauder’s fixed point theorem with a well-posedness theorem when the set C is independent of the state u(i.e.C:=C(t),as presented in[22,23]),we prove the existence of a solution to our quasi-variational fractional sweeping process in infinite-dimensional Hilbert spaces.Similar to the conventional state-dependent sweeping process,achieving this result requires a condition on the size of the Lipschitz constant of the moving set relative to the state.
