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 Freidlin-Wentzell's large deviation principle for the following nonlinear fractional stochastic heat equation driven by Gaussian noise∂/∂tu^(ε)=D_(δ)^(α)(t,x)+√εσ(u^(ε)(t,x))W(t,x...In this paper we study the Freidlin-Wentzell's large deviation principle for the following nonlinear fractional stochastic heat equation driven by Gaussian noise∂/∂tu^(ε)=D_(δ)^(α)(t,x)+√εσ(u^(ε)(t,x))W(t,x),(t,x)∈[0,T]×R,where D_(δ)^(α)is a nonlocal fractional differential operator and W is the Gaussian noise which is white in time and behaves as a fractional Brownian motion with Hurst index H satisfying 3-α/4<H<1/2,in the space variable.The weak convergence approach plays an important role.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 this study,we analyze the convergence of the finite difference method on non-uniform grids and provide examples to demonstrate its effectiveness in approximating fractional differential equations involving the frac...In this study,we analyze the convergence of the finite difference method on non-uniform grids and provide examples to demonstrate its effectiveness in approximating fractional differential equations involving the fractional Laplacian.By utilizing non-uniform grids,it becomes possible to achieve higher accuracy and improved resolution in specific regions of interest.Overall,our findings indicate that finite difference approximation on non-uniform grids can serve as a dependable and efficient tool for approximating fractional Laplacians across a diverse array of applications.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
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
In this paper,we investigate a Dirichlet boundary value problem for a class of fractional degenerate elliptic equations on homogeneous Carnot groups G=(R^(n),o),namely{(-△_(G))^(s)u=f(x,u)+g(x,u)inΩ;u∈H_(0)^(s)(Ω)...In this paper,we investigate a Dirichlet boundary value problem for a class of fractional degenerate elliptic equations on homogeneous Carnot groups G=(R^(n),o),namely{(-△_(G))^(s)u=f(x,u)+g(x,u)inΩ;u∈H_(0)^(s)(Ω),where s∈(0,1),Ω■G is a bounded open domain,(-△_(G))^(s)is the fractional sub-Laplacian,H_(0)^(s)(Ω)denotes the fractional Sobolev space,f(x,u)∈C(Ω×R),g(x,u)is a Carath′eodory function on Ω×R.Using perturbation methods and Morse index estimates in conjunction with fractional Dirichlet eigenvalue estimates,we establish the existence of multiple solutions to the problem.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
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
Calcium-chelating peptide is a new type of calcium supplement with excellent absorption properties and high bioavailability,safety and stability.This study synthesized calcium chelating peptide from gluten by enzymati...Calcium-chelating peptide is a new type of calcium supplement with excellent absorption properties and high bioavailability,safety and stability.This study synthesized calcium chelating peptide from gluten by enzymatic hydrolysis,determined peptide sequences with high activity,and analyzed their digestive characteristics and stability.The enzymatic hydrolysis process was optimized using response surface methodology to determine the optimal enzymatic hydrolysis conditions of temperature 55?C,p H 8.5,and the ratio of alkaline protease to flavor protease(proportion of enzymes)2.63:1 under a liquid-to-solid ratio of 20:1.The calcium chelation rate of gluten hydrolysate was up to 40.1%under the optimal conditions.Fractional purification was then carried out and results showed that peptides with a molecular weight below 500 Da exhibited the highest chelation rate(51.1%).LC-MS/MS analysis was applied to identify 1224 distinct peptide sequences,among which V.YIPPY?C(WCP1)exhibited a higher calcium chelation rate after screening and molecular docking studies.The synthesized WCP1 displayed a calcium chelation rate as high as 53.5%.Fourier Transform Infrared Spectroscopy(FTIR)confirmed that both carboxyl and phosphate groups play crucial roles in mediating interactions between calcium ions and wheat polypeptides.Circular Dichroism(CD)revealed that the structure of wheat peptide became more compact after chelation.Furthermore,stability experiments indicated that the calcium-chelating peptides displayed notable resistance to digestion as well as excellent p H stability and thermal stability.This study provides technical support for deep processing and functional product development of gluten flour.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
In this paper,we investigate the existence and multiplicity of normalized solutions for the following fractional Schrödinger equations{(-△)^(s)u+λu=|u|^(p-2)u-|u|^(q-2)u,x∈R^(N),∫_(R^(N))|u|^(2)dx=c>0,wher...In this paper,we investigate the existence and multiplicity of normalized solutions for the following fractional Schrödinger equations{(-△)^(s)u+λu=|u|^(p-2)u-|u|^(q-2)u,x∈R^(N),∫_(R^(N))|u|^(2)dx=c>0,where N≥2,s∈(0,1),2+4s/N<p<q≤2_(s)^(*)=2N/N-2s,(-△)^(s)represents the fractional Laplacian operator of order s,and the frequencyλ∈R is unknown and appears as a Lagrange multiplier.Specifically,we show that there exists a c>0 such that if c>c,then the problem(P)has at least two normalized solutions,including a normalized ground state solution and a mountain pass type solution.We mainly extend the results in[Commun Pure Appl Anal,2022,21:4113–4145],which dealt with the problem(P)for the case 2<p<q<2+4s/N.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
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Partially supported by NSFC(No.11701304)the K.C.Wong Education Foundation。
文摘In this paper we study the Freidlin-Wentzell's large deviation principle for the following nonlinear fractional stochastic heat equation driven by Gaussian noise∂/∂tu^(ε)=D_(δ)^(α)(t,x)+√εσ(u^(ε)(t,x))W(t,x),(t,x)∈[0,T]×R,where D_(δ)^(α)is a nonlocal fractional differential operator and W is the Gaussian noise which is white in time and behaves as a fractional Brownian motion with Hurst index H satisfying 3-α/4<H<1/2,in the space variable.The weak convergence approach plays an important role.
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 Spanish MINECO through Juan de la Cierva fellow-ship FJC2021-046953-I.
文摘In this study,we analyze the convergence of the finite difference method on non-uniform grids and provide examples to demonstrate its effectiveness in approximating fractional differential equations involving the fractional Laplacian.By utilizing non-uniform grids,it becomes possible to achieve higher accuracy and improved resolution in specific regions of interest.Overall,our findings indicate that finite difference approximation on non-uniform grids can serve as a dependable and efficient tool for approximating fractional Laplacians across a diverse array of applications.
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.
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supported by the NSFC(12131017,12221001)the National Key R&D Program of China(2022YFA1005602)。
文摘In this paper,we investigate a Dirichlet boundary value problem for a class of fractional degenerate elliptic equations on homogeneous Carnot groups G=(R^(n),o),namely{(-△_(G))^(s)u=f(x,u)+g(x,u)inΩ;u∈H_(0)^(s)(Ω),where s∈(0,1),Ω■G is a bounded open domain,(-△_(G))^(s)is the fractional sub-Laplacian,H_(0)^(s)(Ω)denotes the fractional Sobolev space,f(x,u)∈C(Ω×R),g(x,u)is a Carath′eodory function on Ω×R.Using perturbation methods and Morse index estimates in conjunction with fractional Dirichlet eigenvalue estimates,we establish the existence of multiple solutions to the problem.
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.
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Innovation Ability Improvement Project of Science and Technology Small and Medium-sized Enterprises in Shandong Province:2023TSGC0892,2022TSGC2520Project supported by Qingdao Natural Science Foundation:23-2-1-180-zyyd-jch+3 种基金Key R&D Program of Shandong Province,China:2023TZXD078Shandong Province Technology Innovation Guidance Plan:YDZX2023035Qingdao People’s Livelihood Science and Technology Plan Project:23-2-8-xdny-6-nsh,23-3-8-xdny-1-nshThe Two Hundred Talents Project of Yantai City in 2020。
文摘Calcium-chelating peptide is a new type of calcium supplement with excellent absorption properties and high bioavailability,safety and stability.This study synthesized calcium chelating peptide from gluten by enzymatic hydrolysis,determined peptide sequences with high activity,and analyzed their digestive characteristics and stability.The enzymatic hydrolysis process was optimized using response surface methodology to determine the optimal enzymatic hydrolysis conditions of temperature 55?C,p H 8.5,and the ratio of alkaline protease to flavor protease(proportion of enzymes)2.63:1 under a liquid-to-solid ratio of 20:1.The calcium chelation rate of gluten hydrolysate was up to 40.1%under the optimal conditions.Fractional purification was then carried out and results showed that peptides with a molecular weight below 500 Da exhibited the highest chelation rate(51.1%).LC-MS/MS analysis was applied to identify 1224 distinct peptide sequences,among which V.YIPPY?C(WCP1)exhibited a higher calcium chelation rate after screening and molecular docking studies.The synthesized WCP1 displayed a calcium chelation rate as high as 53.5%.Fourier Transform Infrared Spectroscopy(FTIR)confirmed that both carboxyl and phosphate groups play crucial roles in mediating interactions between calcium ions and wheat polypeptides.Circular Dichroism(CD)revealed that the structure of wheat peptide became more compact after chelation.Furthermore,stability experiments indicated that the calcium-chelating peptides displayed notable resistance to digestion as well as excellent p H stability and thermal stability.This study provides technical support for deep processing and functional product development of gluten flour.
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 NNSF of China(12471103)the Natural Science Foundation of Guangdong Province(2024A1515012370)the Guangzhou Basic and Applied Basic Research(2023A04J1316)。
文摘In this paper,we investigate the existence and multiplicity of normalized solutions for the following fractional Schrödinger equations{(-△)^(s)u+λu=|u|^(p-2)u-|u|^(q-2)u,x∈R^(N),∫_(R^(N))|u|^(2)dx=c>0,where N≥2,s∈(0,1),2+4s/N<p<q≤2_(s)^(*)=2N/N-2s,(-△)^(s)represents the fractional Laplacian operator of order s,and the frequencyλ∈R is unknown and appears as a Lagrange multiplier.Specifically,we show that there exists a c>0 such that if c>c,then the problem(P)has at least two normalized solutions,including a normalized ground state solution and a mountain pass type solution.We mainly extend the results in[Commun Pure Appl Anal,2022,21:4113–4145],which dealt with the problem(P)for the case 2<p<q<2+4s/N.
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.
