In this paper,two crossover hybrid variable-order derivatives of the cancer model are developed.Grünwald-Letnikov approximation is used to approximate the hybrid fractional and variable-order fractional operators...In this paper,two crossover hybrid variable-order derivatives of the cancer model are developed.Grünwald-Letnikov approximation is used to approximate the hybrid fractional and variable-order fractional operators.The existence,uniqueness,and stability of the proposed model are discussed.Adams Bashfourth’s fifth-step method with a hybrid variable-order fractional operator is developed to study the proposed models.Comparative studies with generalized fifth-order Runge-Kutta method are given.Numerical examples and comparative studies to verify the applicability of the used methods and to demonstrate the simplicity of these approximations are presented.We have showcased the efficiency of the proposed method and garnered robust empirical support for our theoretical findings.展开更多
In recent years,fractional-order chaotic maps have been paid more attention in publications because of the memory effect.This paper presents a novel variable-order fractional sine map(VFSM)based on the discrete fracti...In recent years,fractional-order chaotic maps have been paid more attention in publications because of the memory effect.This paper presents a novel variable-order fractional sine map(VFSM)based on the discrete fractional calculus.Specially,the order is defined as an iterative function that incorporates the current state of the system.By analyzing phase diagrams,time sequences,bifurcations,Lyapunov exponents and fuzzy entropy complexity,the dynamics of the proposed map are investigated comparing with the constant-order fractional sine map.The results reveal that the variable order has a good effect on improving the chaotic performance,and it enlarges the range of available parameter values as well as reduces non-chaotic windows.Multiple coexisting attractors also enrich the dynamics of VFSM and prove its sensitivity to initial values.Moreover,the sequence generated by the proposed map passes the statistical test for pseudorandom number and shows strong robustness to parameter estimation,which proves the potential applications in the field of information security.展开更多
This paper is concerned with the following variable-order fractional Laplacian equations , where N ≥ 1 and N > 2s(x,y) for (x,y) ∈ Ω × Ω, Ω is a bounded domain in R<sup>N</sup>, s(⋅)...This paper is concerned with the following variable-order fractional Laplacian equations , where N ≥ 1 and N > 2s(x,y) for (x,y) ∈ Ω × Ω, Ω is a bounded domain in R<sup>N</sup>, s(⋅) ∈ C (R<sup>N</sup> × R<sup>N</sup>, (0,1)), (-Δ)<sup>s(⋅)</sup> is the variable-order fractional Laplacian operator, λ, μ > 0 are two parameters, V: Ω → [0, ∞) is a continuous function, f ∈ C(Ω × R) and q ∈ C(Ω). Under some suitable conditions on f, we obtain two solutions for this problem by employing the mountain pass theorem and Ekeland’s variational principle. Our result generalizes the related ones in the literature.展开更多
In this paper, we study the solutions for variable-order time-fractional diffusion equations. A three-point combined compact difference (CCD) method is used to discretize the spatial variables to achieve sixth-order a...In this paper, we study the solutions for variable-order time-fractional diffusion equations. A three-point combined compact difference (CCD) method is used to discretize the spatial variables to achieve sixth-order accuracy, while the exponential-sum-approximation (ESA) is used to approximate the variable-order Caputo fractional derivative in the temporal direction, and a novel spatial sixth-order hybrid ESA-CCD method is implemented successfully. Finally, the accuracy of the proposed method is verified by numerical experiments.展开更多
Nonlinear fractional differential equations provide suitable models to describe real-world phenomena and many fractional derivatives are varying with time and space.The present study considers the advanced and broad s...Nonlinear fractional differential equations provide suitable models to describe real-world phenomena and many fractional derivatives are varying with time and space.The present study considers the advanced and broad spectrum of the nonlinear(NL)variable-order fractional differential equation(VO-FDE)in sense of VO Caputo fractional derivative(CFD)to describe the physical models.The VO-FDE transforms into an ordinary differential equation(ODE)and then solving by the modified(G/G)-expansion method.For ac-curacy,the space-time VO fractional Korteweg-de Vries(KdV)equation is solved by the proposed method and obtained some new types of periodic wave,singular,and Kink exact solutions.The newly obtained solutions confirmed that the proposed method is well-ordered and capable implement to find a class of NL-VO equations.The VO non-integer performance of the solutions is studied broadly by using 2D and 3D graphical representation.The results revealed that the NL VO-FDEs are highly active,functional and convenient in explaining the problems in scientific physics.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
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
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
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 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
In recent years,variable-order fractional partial differential equations have attracted growing interest due to their enhanced ability tomodel complex physical phenomena withmemory and spatial heterogeneity.However,ex...In recent years,variable-order fractional partial differential equations have attracted growing interest due to their enhanced ability tomodel complex physical phenomena withmemory and spatial heterogeneity.However,existing numerical methods often struggle with the computational challenges posed by such equations,especially in nonlinear,multi-term formulations.This study introduces two hybrid numerical methods—the Linear-Sine and Cosine(L1-CAS)and fast-CAS schemes—for solving linear and nonlinear multi-term Caputo variable-order(CVO)fractional partial differential equations.These methods combine CAS wavelet-based spatial discretization with L1 and fast algorithms in the time domain.A key feature of the approach is its ability to efficiently handle fully coupled spacetime variable-order derivatives and nonlinearities through a second-order interpolation technique.In addition,we derive CAS wavelet operational matrices for variable-order integration and for boundary value problems,forming the foundation of the spatial discretization.Numerical experiments confirm the accuracy,stability,and computational efficiency of the proposed methods.展开更多
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
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 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 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
We study the Cauchy problem of the fractional Kramers-Fokker-Planck equation with moderate soft potential and show that the solution to the Cauchy problem enjoys an analytic Gelfand-Shilov regularizing effect for posi...We study the Cauchy problem of the fractional Kramers-Fokker-Planck equation with moderate soft potential and show that the solution to the Cauchy problem enjoys an analytic Gelfand-Shilov regularizing effect for positive time.展开更多
The long-term Mittag-Leffler stability of solutions to multi-term timefractional diffusion equations with constant coefficients was rigorously established,which demonstrated that the algebraic decay rate of the soluti...The long-term Mittag-Leffler stability of solutions to multi-term timefractional diffusion equations with constant coefficients was rigorously established,which demonstrated that the algebraic decay rate of the solution,characterized by||u_(n)||L^(2)(Ω)=O(t^(−αs)) as t→∞,is determined by the minimum order α_(s) of the time-fractional derivatives.Building on this foundational result,this article pursues two primary objectives.First,we introduce a strongly A-stable fractional linear multistep method and derive the numerical stability region for the governing equation.Second,we rigorously prove the long-term decay rate of the numerical solution through a detailed singularity analysis of its generating function.Notably,the numerical decay rate||u_(n)||L^(2)(Ω)=O(t_(n)^(−α_(s)) as t_(n)→∞aligns precisely with the continuous case.Theoretical findings are further validated through comprehensive numerical simulations,underscoring the robustness of our proposed method.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
文摘In this paper,two crossover hybrid variable-order derivatives of the cancer model are developed.Grünwald-Letnikov approximation is used to approximate the hybrid fractional and variable-order fractional operators.The existence,uniqueness,and stability of the proposed model are discussed.Adams Bashfourth’s fifth-step method with a hybrid variable-order fractional operator is developed to study the proposed models.Comparative studies with generalized fifth-order Runge-Kutta method are given.Numerical examples and comparative studies to verify the applicability of the used methods and to demonstrate the simplicity of these approximations are presented.We have showcased the efficiency of the proposed method and garnered robust empirical support for our theoretical findings.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.62071496,61901530,and 62061008)the Natural Science Foundation of Hunan Province of China(Grant No.2020JJ5767).
文摘In recent years,fractional-order chaotic maps have been paid more attention in publications because of the memory effect.This paper presents a novel variable-order fractional sine map(VFSM)based on the discrete fractional calculus.Specially,the order is defined as an iterative function that incorporates the current state of the system.By analyzing phase diagrams,time sequences,bifurcations,Lyapunov exponents and fuzzy entropy complexity,the dynamics of the proposed map are investigated comparing with the constant-order fractional sine map.The results reveal that the variable order has a good effect on improving the chaotic performance,and it enlarges the range of available parameter values as well as reduces non-chaotic windows.Multiple coexisting attractors also enrich the dynamics of VFSM and prove its sensitivity to initial values.Moreover,the sequence generated by the proposed map passes the statistical test for pseudorandom number and shows strong robustness to parameter estimation,which proves the potential applications in the field of information security.
文摘This paper is concerned with the following variable-order fractional Laplacian equations , where N ≥ 1 and N > 2s(x,y) for (x,y) ∈ Ω × Ω, Ω is a bounded domain in R<sup>N</sup>, s(⋅) ∈ C (R<sup>N</sup> × R<sup>N</sup>, (0,1)), (-Δ)<sup>s(⋅)</sup> is the variable-order fractional Laplacian operator, λ, μ > 0 are two parameters, V: Ω → [0, ∞) is a continuous function, f ∈ C(Ω × R) and q ∈ C(Ω). Under some suitable conditions on f, we obtain two solutions for this problem by employing the mountain pass theorem and Ekeland’s variational principle. Our result generalizes the related ones in the literature.
文摘In this paper, we study the solutions for variable-order time-fractional diffusion equations. A three-point combined compact difference (CCD) method is used to discretize the spatial variables to achieve sixth-order accuracy, while the exponential-sum-approximation (ESA) is used to approximate the variable-order Caputo fractional derivative in the temporal direction, and a novel spatial sixth-order hybrid ESA-CCD method is implemented successfully. Finally, the accuracy of the proposed method is verified by numerical experiments.
文摘Nonlinear fractional differential equations provide suitable models to describe real-world phenomena and many fractional derivatives are varying with time and space.The present study considers the advanced and broad spectrum of the nonlinear(NL)variable-order fractional differential equation(VO-FDE)in sense of VO Caputo fractional derivative(CFD)to describe the physical models.The VO-FDE transforms into an ordinary differential equation(ODE)and then solving by the modified(G/G)-expansion method.For ac-curacy,the space-time VO fractional Korteweg-de Vries(KdV)equation is solved by the proposed method and obtained some new types of periodic wave,singular,and Kink exact solutions.The newly obtained solutions confirmed that the proposed method is well-ordered and capable implement to find a class of NL-VO equations.The VO non-integer performance of the solutions is studied broadly by using 2D and 3D graphical representation.The results revealed that the NL VO-FDEs are highly active,functional and convenient in explaining the problems in scientific physics.
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.
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.
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supported by the National Research Foundation of Korea(NRF)grant funded by the Korean government(MSIT)(NRF-2021R1A2C1011817)the BK21 Program(Next Generation Education Program for Mathematical Sciences,4299990414089)funded by the Ministry of Education(MOE,Republic of Korea).
文摘In recent years,variable-order fractional partial differential equations have attracted growing interest due to their enhanced ability tomodel complex physical phenomena withmemory and spatial heterogeneity.However,existing numerical methods often struggle with the computational challenges posed by such equations,especially in nonlinear,multi-term formulations.This study introduces two hybrid numerical methods—the Linear-Sine and Cosine(L1-CAS)and fast-CAS schemes—for solving linear and nonlinear multi-term Caputo variable-order(CVO)fractional partial differential equations.These methods combine CAS wavelet-based spatial discretization with L1 and fast algorithms in the time domain.A key feature of the approach is its ability to efficiently handle fully coupled spacetime variable-order derivatives and nonlinearities through a second-order interpolation technique.In addition,we derive CAS wavelet operational matrices for variable-order integration and for boundary value problems,forming the foundation of the spatial discretization.Numerical experiments confirm the accuracy,stability,and computational efficiency of the proposed methods.
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.
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Supported by the National Natural Science Foundation of China (Grant No.12031006)the Fundamental Research Funds for the Central Universities of China。
文摘We study the Cauchy problem of the fractional Kramers-Fokker-Planck equation with moderate soft potential and show that the solution to the Cauchy problem enjoys an analytic Gelfand-Shilov regularizing effect for positive time.
文摘The long-term Mittag-Leffler stability of solutions to multi-term timefractional diffusion equations with constant coefficients was rigorously established,which demonstrated that the algebraic decay rate of the solution,characterized by||u_(n)||L^(2)(Ω)=O(t^(−αs)) as t→∞,is determined by the minimum order α_(s) of the time-fractional derivatives.Building on this foundational result,this article pursues two primary objectives.First,we introduce a strongly A-stable fractional linear multistep method and derive the numerical stability region for the governing equation.Second,we rigorously prove the long-term decay rate of the numerical solution through a detailed singularity analysis of its generating function.Notably,the numerical decay rate||u_(n)||L^(2)(Ω)=O(t_(n)^(−α_(s)) as t_(n)→∞aligns precisely with the continuous case.Theoretical findings are further validated through comprehensive numerical simulations,underscoring the robustness of our proposed method.
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.
