In this paper,we investigate the controllability for neutral stochastic evolution equations driven by fractional Brownian motion with Hurst parameter H ∈（1/2,1） in a Hilbert space.We employ the α-norm in order to ...In this paper,we investigate the controllability for neutral stochastic evolution equations driven by fractional Brownian motion with Hurst parameter H ∈（1/2,1） in a Hilbert space.We employ the α-norm in order to reflect the relationship between H and the fractional power α.Sufficient conditions are established by using stochastic analysis theory and operator theory.An example is provided to illustrate the effectiveness of the proposed result.展开更多
In this article,some high-order local discontinuous Galerkin(LDG)schemes based on some second-order θ approximation formulas in time are presented to solve a two-dimen-sional nonlinear fractional diffusion equation.T...In this article,some high-order local discontinuous Galerkin(LDG)schemes based on some second-order θ approximation formulas in time are presented to solve a two-dimen-sional nonlinear fractional diffusion equation.The unconditional stability of the LDG scheme is proved,and an a priori error estimate with O(h^(k+1)+At^(2))is derived,where k≥0 denotes the index of the basis function.Extensive numerical results with Q^(k)(k=0,1,2,3)elements are provided to confirm our theoretical results,which also show that the second-order convergence rate in time is not impacted by the changed parameter θ.展开更多
In this paper, we investigate a class of abstract neutral fractional delayed evolution equation in the fractional power space. With the aid of the analytic semigroup theories and some fixed point theorems, we establis...In this paper, we investigate a class of abstract neutral fractional delayed evolution equation in the fractional power space. With the aid of the analytic semigroup theories and some fixed point theorems, we establish the existence and uniqueness of the S-asymptotically periodic α-mild solutions. The linear part generates a compact and exponentially stable analytic semigroup and the nonlinear parts satisfy some conditions with respect to the fractional power norm of the linear part, which greatly improve and generalize the relevant results of existing literatures.展开更多
Stochastic fractional differential systems are important and useful in the mathematics,physics,and engineering fields.However,the determination of their probabilistic responses is difficult due to their non-Markovian ...Stochastic fractional differential systems are important and useful in the mathematics,physics,and engineering fields.However,the determination of their probabilistic responses is difficult due to their non-Markovian property.The recently developed globally-evolving-based generalized density evolution equation(GE-GDEE),which is a unified partial differential equation(PDE)governing the transient probability density function(PDF)of a generic path-continuous process,including non-Markovian ones,provides a feasible tool to solve this problem.In the paper,the GE-GDEE for multi-dimensional linear fractional differential systems subject to Gaussian white noise is established.In particular,it is proved that in the GE-GDEE corresponding to the state-quantities of interest,the intrinsic drift coefficient is a time-varying linear function,and can be analytically determined.In this sense,an alternative low-dimensional equivalent linear integer-order differential system with exact closed-form coefficients for the original highdimensional linear fractional differential system can be constructed such that their transient PDFs are identical.Specifically,for a multi-dimensional linear fractional differential system,if only one or two quantities are of interest,GE-GDEE is only in one or two dimensions,and the surrogate system would be a one-or two-dimensional linear integer-order system.Several examples are studied to assess the merit of the proposed method.Though presently the closed-form intrinsic drift coefficient is only available for linear stochastic fractional differential systems,the findings in the present paper provide a remarkable demonstration on the existence and eligibility of GE-GDEE for the case that the original high-dimensional system itself is non-Markovian,and provide insights for the physical-mechanism-informed determination of intrinsic drift and diffusion coefficients of GE-GDEE of more generic complex nonlinear systems.展开更多
For two-dimensional(2D)time fractional diffusion equations,we construct a numerical method based on a local discontinuous Galerkin(LDG)method in space and a finite differ-ence scheme in time.We investigate the numeric...For two-dimensional(2D)time fractional diffusion equations,we construct a numerical method based on a local discontinuous Galerkin(LDG)method in space and a finite differ-ence scheme in time.We investigate the numerical stability and convergence of the method for both rectangular and triangular meshes and show that the method is unconditionally stable.Numerical results indicate the effectiveness and accuracy of the method and con-firm the analysis.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
This article deals with a new fractional nonlinear delay evolution system driven by a hemi-variational inequality in a Banach space.Utilizing the KKM theorem,a result concerned with the upper semicontinuity and measur...This article deals with a new fractional nonlinear delay evolution system driven by a hemi-variational inequality in a Banach space.Utilizing the KKM theorem,a result concerned with the upper semicontinuity and measurability of the solution set of a hemivariational inequality is established.By using a fixed point theorem for a condensing setvalued map,the nonemptiness and compactness of the set of mild solutions are also obtained for such a system under mild conditions.Finally,an example is presented to illustrate our main results.展开更多
In this article, we investigate some exact wave solutions to the higher dimensional time-fractional Schrodinger equation, an important equation in quantum mechanics. The fractional Schrodinger equation further precise...In this article, we investigate some exact wave solutions to the higher dimensional time-fractional Schrodinger equation, an important equation in quantum mechanics. The fractional Schrodinger equation further precisely describes the quantum state of a physical system changes in time. In order to determine the solutions a suitable transformation is considered to transmute the equations into a simpler ordinary differential equation (ODE) namely fractional complex transformation. We then use the modified simple equation (MSE) method to obtain new and further general exact wave solutions. The MSE method is more powerful and can be used in other works to establish completely new solutions for other kind of nonlinear fractional differential equations arising in mathematical physics. The affect of obtaining parameters for its definite values which are examined from the solutions of two dimensional and three dimensional time-fractional Schrodinger equations are discussed and therefore might be useful in different physical applications where the equations arise in this article.展开更多
In this paper,we firstly recall some basic results on pseudo S-asymptotically(ω,c)-periodic functions and Sobolev type fractional differential equation.We secondly investigate some existence of pseudo S-asymptotical...In this paper,we firstly recall some basic results on pseudo S-asymptotically(ω,c)-periodic functions and Sobolev type fractional differential equation.We secondly investigate some existence of pseudo S-asymptotically(ω,c)-periodic solutions for a semilinear fractional differential equations of Sobolev type.We finally present a simple example.展开更多
In this paper,the regularity and finite difference methods for the two-dimensional delay fractional equations are considered.The analytic solution is derived by eigenvalue expansions and Laplace transformation.However...In this paper,the regularity and finite difference methods for the two-dimensional delay fractional equations are considered.The analytic solution is derived by eigenvalue expansions and Laplace transformation.However,due to the derivative discontinuities resulting from the delay effect,the traditional L1-ADI scheme fails to achieve the optimal convergence order.To overcome this issue and improve the convergence order,a simple and cost-effective decomposition technique is introduced and a fitted L1-ADI scheme is proposed.The numerical tests are conducted to verify the theoretical result.展开更多
In this work,we investigate the existence and asymptotic stability in mean square of mild solutions for non-linear impulsive neutral stochastic evolution equations with infinite delays in distribution in a real separa...In this work,we investigate the existence and asymptotic stability in mean square of mild solutions for non-linear impulsive neutral stochastic evolution equations with infinite delays in distribution in a real separable Hilbert space.By using the Banach fixed point principle,some sufficient conditions are derived to ensure the asymptotic stability of mild solutions.Moreover,we investigate the Hyers-Ulam stability for such stochastic system.Finally,an illustrative example is given to demonstrate the effectiveness of the obtained results.展开更多
The paper deals with the obliquely propagating wave solutions of fractional nonlinear evolution equations(NLEEs)arising in science and engineering.The conformable time fractional(2+1)-dimensional extended Zakharov-Kuz...The paper deals with the obliquely propagating wave solutions of fractional nonlinear evolution equations(NLEEs)arising in science and engineering.The conformable time fractional(2+1)-dimensional extended Zakharov-Kuzetsov equation(EZKE),coupled space-time fractional(2+1)-dimensional dispersive long wave equation(DLWE)and space-time fractional(2+1)-dimensional Ablowitz-Kaup-Newell-Segur(AKNS)equation are considered to investigate such physical phenomena.The modified Kudryashov method along with the properties of conformable and modified Riemann-Liouville derivatives is employed to construct the oblique wave solutions of the considered equations.The obtained results may be useful for better understanding the nature of internal oblique propagating wave dynamics in ocean engineering.展开更多
This paper investigates the nonemptiness and compactness of the mild solution set for a class of Riemann-Liouville fractional delay differential variational inequalities,which are formulated by a Riemann-Liouville fra...This paper investigates the nonemptiness and compactness of the mild solution set for a class of Riemann-Liouville fractional delay differential variational inequalities,which are formulated by a Riemann-Liouville fractional delay evolution equation and a variational inequality.Our approach is based on the resolvent technique and a generalization of strongly continuous semigroups combined with Schauder's fixed point theorem.展开更多
Based on the equivalent integro-differential form of the considered problem, a numerical approach to solving the two-dimensional nonlinear time fractional wave equations(NTFWEs) is considered in this paper. To this en...Based on the equivalent integro-differential form of the considered problem, a numerical approach to solving the two-dimensional nonlinear time fractional wave equations(NTFWEs) is considered in this paper. To this end, an alternating direction implicit(ADI) numerical scheme is derived. The scheme is established by combining the secondorder convolution quadrature formula and Crank–Nicolson technique in time and afourth-order difference approach in space. The convergence and unconditional stability of the proposed compact ADI scheme are strictly discussed after a concise solvabilityanalysis. A numerical example is shown to demonstrate the theoretical analysis.展开更多
In this paper we consider a class of fractional order evolution equations which interpolates the heat equation and wave equation. By Mittag-Lefflers functions[1] and functions transform the representative formula of s...In this paper we consider a class of fractional order evolution equations which interpolates the heat equation and wave equation. By Mittag-Lefflers functions[1] and functions transform the representative formula of solution for fractional evolution equation is obtained. Further we give a theoretical description for fractional evolution equation from the integrated semigroup point of view.展开更多
In this paper,we consider the existence and uniqueness of the mild solutions for a class of fractional non-autonomous evolution equations with delay and Caputo's fractional derivatives.By using the measure of nonc...In this paper,we consider the existence and uniqueness of the mild solutions for a class of fractional non-autonomous evolution equations with delay and Caputo's fractional derivatives.By using the measure of noncompactness,β-resolvent family,fixed point theorems and Banach contraction mapping principle,we improve and generalizes some related results on this topic.At last,we give an example to illustrate the application of the main results of this paper.展开更多
The aim of this paper is to consider the convergence of the numerical methods for stochastic time-fractional evolution equations driven by fractional Brownian motion.The spatial and temporal regularity of the mild sol...The aim of this paper is to consider the convergence of the numerical methods for stochastic time-fractional evolution equations driven by fractional Brownian motion.The spatial and temporal regularity of the mild solution is given.The numerical scheme approximates the problem in space by the Galerkin finite element method and in time by the backward Euler convolution quadrature formula,and the noise by the L 2-projection.The strong convergence error estimates for both semi-discrete and fully discrete schemes are established.A numerical example is presented to verify our theoretical analysis.展开更多
The void evolution equation and the elastoplastic constitutive model of casting magnesium alloy were investigated. The void evolution equation consists of the void growth and the void nucleation equations. The void gr...The void evolution equation and the elastoplastic constitutive model of casting magnesium alloy were investigated. The void evolution equation consists of the void growth and the void nucleation equations. The void growth equation was obtained based on the continuous supposition of the material matrix,and the void nucleation equation was derived by assuming that the void nucleation follows a normal distribution. A softening function related to the void evolution was given. After the softening function was embedded to a nonclassical elastoplastic constitutive equation,a constitutive model involving void evolution was obtained. The numerical algorithm and the finite element procedure related to the constitutive model were developed and applied to the analysis of the distributions of the stress and the porosity of the notched cylindrical specimens of casting magnesium alloy ZL305. The computed results show satisfactory agreement with the experimental data.展开更多
基金supported by NSFC(11271020,11401010)Natural Science Foundation of Anhui Province(1308085QA14)+1 种基金supported by NSFC(11571071)Innovation Program of Shanghai Municipal Education Commission(12ZZ063)
文摘In this paper,we investigate the controllability for neutral stochastic evolution equations driven by fractional Brownian motion with Hurst parameter H ∈（1/2,1） in a Hilbert space.We employ the α-norm in order to reflect the relationship between H and the fractional power α.Sufficient conditions are established by using stochastic analysis theory and operator theory.An example is provided to illustrate the effectiveness of the proposed result.
基金This work is supported by the National Natural Science Foundation of China(11661058,11761053)the Natural Science Foundation of Inner Mongolia(2017MS0107)the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region(NJYT-17-A07).
文摘In this article,some high-order local discontinuous Galerkin(LDG)schemes based on some second-order θ approximation formulas in time are presented to solve a two-dimen-sional nonlinear fractional diffusion equation.The unconditional stability of the LDG scheme is proved,and an a priori error estimate with O(h^(k+1)+At^(2))is derived,where k≥0 denotes the index of the basis function.Extensive numerical results with Q^(k)(k=0,1,2,3)elements are provided to confirm our theoretical results,which also show that the second-order convergence rate in time is not impacted by the changed parameter θ.
基金Supported by NNSF of China(11871302)China Postdoctoral Science Foundation(2020M682140)+1 种基金NSF of Shanxi,China (201901D211399)Graduate Research Support project of Northwest Normal University(2021KYZZ01030)
文摘In this paper, we investigate a class of abstract neutral fractional delayed evolution equation in the fractional power space. With the aid of the analytic semigroup theories and some fixed point theorems, we establish the existence and uniqueness of the S-asymptotically periodic α-mild solutions. The linear part generates a compact and exponentially stable analytic semigroup and the nonlinear parts satisfy some conditions with respect to the fractional power norm of the linear part, which greatly improve and generalize the relevant results of existing literatures.
基金The supports of the National Natural Science Foundation of China(Grant Nos.51725804 and U1711264)the Research Fund for State Key Laboratories of Ministry of Science and Technology of China(SLDRCE19-B-23)the Shanghai Post-Doctoral Excellence Program(2022558)。
文摘Stochastic fractional differential systems are important and useful in the mathematics,physics,and engineering fields.However,the determination of their probabilistic responses is difficult due to their non-Markovian property.The recently developed globally-evolving-based generalized density evolution equation(GE-GDEE),which is a unified partial differential equation(PDE)governing the transient probability density function(PDF)of a generic path-continuous process,including non-Markovian ones,provides a feasible tool to solve this problem.In the paper,the GE-GDEE for multi-dimensional linear fractional differential systems subject to Gaussian white noise is established.In particular,it is proved that in the GE-GDEE corresponding to the state-quantities of interest,the intrinsic drift coefficient is a time-varying linear function,and can be analytically determined.In this sense,an alternative low-dimensional equivalent linear integer-order differential system with exact closed-form coefficients for the original highdimensional linear fractional differential system can be constructed such that their transient PDFs are identical.Specifically,for a multi-dimensional linear fractional differential system,if only one or two quantities are of interest,GE-GDEE is only in one or two dimensions,and the surrogate system would be a one-or two-dimensional linear integer-order system.Several examples are studied to assess the merit of the proposed method.Though presently the closed-form intrinsic drift coefficient is only available for linear stochastic fractional differential systems,the findings in the present paper provide a remarkable demonstration on the existence and eligibility of GE-GDEE for the case that the original high-dimensional system itself is non-Markovian,and provide insights for the physical-mechanism-informed determination of intrinsic drift and diffusion coefficients of GE-GDEE of more generic complex nonlinear systems.
文摘For two-dimensional(2D)time fractional diffusion equations,we construct a numerical method based on a local discontinuous Galerkin(LDG)method in space and a finite differ-ence scheme in time.We investigate the numerical stability and convergence of the method for both rectangular and triangular meshes and show that the method is unconditionally stable.Numerical results indicate the effectiveness and accuracy of the method and con-firm the analysis.
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supported by the National Natural Science Foundation of China(11471230,11671282)。
文摘This article deals with a new fractional nonlinear delay evolution system driven by a hemi-variational inequality in a Banach space.Utilizing the KKM theorem,a result concerned with the upper semicontinuity and measurability of the solution set of a hemivariational inequality is established.By using a fixed point theorem for a condensing setvalued map,the nonemptiness and compactness of the set of mild solutions are also obtained for such a system under mild conditions.Finally,an example is presented to illustrate our main results.
文摘In this article, we investigate some exact wave solutions to the higher dimensional time-fractional Schrodinger equation, an important equation in quantum mechanics. The fractional Schrodinger equation further precisely describes the quantum state of a physical system changes in time. In order to determine the solutions a suitable transformation is considered to transmute the equations into a simpler ordinary differential equation (ODE) namely fractional complex transformation. We then use the modified simple equation (MSE) method to obtain new and further general exact wave solutions. The MSE method is more powerful and can be used in other works to establish completely new solutions for other kind of nonlinear fractional differential equations arising in mathematical physics. The affect of obtaining parameters for its definite values which are examined from the solutions of two dimensional and three dimensional time-fractional Schrodinger equations are discussed and therefore might be useful in different physical applications where the equations arise in this article.
基金supported by NSF of Shaanxi Province(Grant No.2023-JC-YB-011).
文摘In this paper,we firstly recall some basic results on pseudo S-asymptotically(ω,c)-periodic functions and Sobolev type fractional differential equation.We secondly investigate some existence of pseudo S-asymptotically(ω,c)-periodic solutions for a semilinear fractional differential equations of Sobolev type.We finally present a simple example.
基金supported by University of Macao(File nos.MYRG2020-00035-FST,MYRG2022-00076-FST,MYRG2022-00262-FST).
文摘In this paper,the regularity and finite difference methods for the two-dimensional delay fractional equations are considered.The analytic solution is derived by eigenvalue expansions and Laplace transformation.However,due to the derivative discontinuities resulting from the delay effect,the traditional L1-ADI scheme fails to achieve the optimal convergence order.To overcome this issue and improve the convergence order,a simple and cost-effective decomposition technique is introduced and a fitted L1-ADI scheme is proposed.The numerical tests are conducted to verify the theoretical result.
基金supported by the Excellent Talents Support Program for Colleges and Universities in Anhui Province(Grant No.gxyqZD2020003)。
文摘In this work,we investigate the existence and asymptotic stability in mean square of mild solutions for non-linear impulsive neutral stochastic evolution equations with infinite delays in distribution in a real separable Hilbert space.By using the Banach fixed point principle,some sufficient conditions are derived to ensure the asymptotic stability of mild solutions.Moreover,we investigate the Hyers-Ulam stability for such stochastic system.Finally,an illustrative example is given to demonstrate the effectiveness of the obtained results.
文摘The paper deals with the obliquely propagating wave solutions of fractional nonlinear evolution equations(NLEEs)arising in science and engineering.The conformable time fractional(2+1)-dimensional extended Zakharov-Kuzetsov equation(EZKE),coupled space-time fractional(2+1)-dimensional dispersive long wave equation(DLWE)and space-time fractional(2+1)-dimensional Ablowitz-Kaup-Newell-Segur(AKNS)equation are considered to investigate such physical phenomena.The modified Kudryashov method along with the properties of conformable and modified Riemann-Liouville derivatives is employed to construct the oblique wave solutions of the considered equations.The obtained results may be useful for better understanding the nature of internal oblique propagating wave dynamics in ocean engineering.
基金supported by the National Natural Science Foundation of China(11772306)Natural Science Foundation of Guangxi Province(2018GXNSFAA281021)+2 种基金Guangxi Science and Technology Base Foundation(AD20159017)the Foundation of Guilin University of Technology(GUTQDJJ2017062)the Fundamental Research Funds for the Central Universities,China University of Geosciences(Wuhan)(CUGGC05).
文摘This paper investigates the nonemptiness and compactness of the mild solution set for a class of Riemann-Liouville fractional delay differential variational inequalities,which are formulated by a Riemann-Liouville fractional delay evolution equation and a variational inequality.Our approach is based on the resolvent technique and a generalization of strongly continuous semigroups combined with Schauder's fixed point theorem.
基金This survey is supported by the National Natural Science Foundation of China(Grant No.11371029)the Quality Engineering Project of Colleges and Universities in Anhui Province(Grant No.2018kfk136).
文摘Based on the equivalent integro-differential form of the considered problem, a numerical approach to solving the two-dimensional nonlinear time fractional wave equations(NTFWEs) is considered in this paper. To this end, an alternating direction implicit(ADI) numerical scheme is derived. The scheme is established by combining the secondorder convolution quadrature formula and Crank–Nicolson technique in time and afourth-order difference approach in space. The convergence and unconditional stability of the proposed compact ADI scheme are strictly discussed after a concise solvabilityanalysis. A numerical example is shown to demonstrate the theoretical analysis.
文摘In this paper we consider a class of fractional order evolution equations which interpolates the heat equation and wave equation. By Mittag-Lefflers functions[1] and functions transform the representative formula of solution for fractional evolution equation is obtained. Further we give a theoretical description for fractional evolution equation from the integrated semigroup point of view.
基金The paper is supported financially by the Project of Shandong Province Higher Educational Science and Technology Program(J16LI14)the National Natural Science Foundation of China(No.11871302)+2 种基金the Taishan Scholars Program of Shandong Province(No.tsqn20161041)the Humanities and Social Sciences Project of the Ministry Education of China(No.19YJA910002)the Natural Science Foundation of Shandong Province(No.ZR2018MG002).
文摘In this paper,we consider the existence and uniqueness of the mild solutions for a class of fractional non-autonomous evolution equations with delay and Caputo's fractional derivatives.By using the measure of noncompactness,β-resolvent family,fixed point theorems and Banach contraction mapping principle,we improve and generalizes some related results on this topic.At last,we give an example to illustrate the application of the main results of this paper.
文摘The aim of this paper is to consider the convergence of the numerical methods for stochastic time-fractional evolution equations driven by fractional Brownian motion.The spatial and temporal regularity of the mild solution is given.The numerical scheme approximates the problem in space by the Galerkin finite element method and in time by the backward Euler convolution quadrature formula,and the noise by the L 2-projection.The strong convergence error estimates for both semi-discrete and fully discrete schemes are established.A numerical example is presented to verify our theoretical analysis.
基金Project(10572157) supported by the National Natural Science Foundation of China
文摘The void evolution equation and the elastoplastic constitutive model of casting magnesium alloy were investigated. The void evolution equation consists of the void growth and the void nucleation equations. The void growth equation was obtained based on the continuous supposition of the material matrix,and the void nucleation equation was derived by assuming that the void nucleation follows a normal distribution. A softening function related to the void evolution was given. After the softening function was embedded to a nonclassical elastoplastic constitutive equation,a constitutive model involving void evolution was obtained. The numerical algorithm and the finite element procedure related to the constitutive model were developed and applied to the analysis of the distributions of the stress and the porosity of the notched cylindrical specimens of casting magnesium alloy ZL305. The computed results show satisfactory agreement with the experimental data.
