This article concerns the construction of approximate solutions for a general stochastic integrodifferential equation which is not explicitly solvable and whose coeffcients functionally depend on Lebesgue integrals an...This article concerns the construction of approximate solutions for a general stochastic integrodifferential equation which is not explicitly solvable and whose coeffcients functionally depend on Lebesgue integrals and stochastic integrals with respect to martingales. The approximate equations are linear ordinary stochastic differential equations, the solutions of which are defined on sub-intervals of an arbitrary partition of the time interval and connected at successive division points. The closeness of the initial and approximate solutions is measured in the L^p-th norm, uniformly on the time interval. The convergence with probability one is also given.展开更多
A nonlinear fractional integrodifferential equation with three-point fractional bound- ary conditions is studied in this paper, and some sufficient conditions for existence and u- niqueness of solutions for the equati...A nonlinear fractional integrodifferential equation with three-point fractional bound- ary conditions is studied in this paper, and some sufficient conditions for existence and u- niqueness of solutions for the equation are established by Krasnoselskii fixed point theorem and Banach contraction principle, respectively.展开更多
Using Daher's fixed point theorem, we obtain a local existence theorem, in which the assumption is weaker than That in the Theorem 2.1 in [2]. Based on this theorem, we get a global existence theorem which is an e...Using Daher's fixed point theorem, we obtain a local existence theorem, in which the assumption is weaker than That in the Theorem 2.1 in [2]. Based on this theorem, we get a global existence theorem which is an extension of certain results for ordinary differential equations.展开更多
In this Paper. by using the pseudo-spectral method of Fornberg and Whitham, a nonlinear integrodifferential equations is investigated numerically. It is found that for small ∈, the result is close to that of the KdV ...In this Paper. by using the pseudo-spectral method of Fornberg and Whitham, a nonlinear integrodifferential equations is investigated numerically. It is found that for small ∈, the result is close to that of the KdV equation, whereas the effects of larger ∈ and the initial condition are significant.展开更多
In this paper, we concertrate our efforts on discuss asymptotic stability of linear inte grodifferential systems with time-varied confficients with large scale via Liapunov functional and decomposite - aggregated meth...In this paper, we concertrate our efforts on discuss asymptotic stability of linear inte grodifferential systems with time-varied confficients with large scale via Liapunov functional and decomposite - aggregated method. A group of sufficient conditions are given to guarantee asymptotic stability of zero solutions of systems.展开更多
In this paper we prove the existence of mild solutions of a general class of nonlinear evolution integrodifferential equation in Banach spaces. Based on the resolvent operator and the Schaefer fixed point theorem, a s...In this paper we prove the existence of mild solutions of a general class of nonlinear evolution integrodifferential equation in Banach spaces. Based on the resolvent operator and the Schaefer fixed point theorem, a sufficient condition for the existence of general integrodifferential evolution equations is established.展开更多
A fixed point analysis approach is used to investigate the existence of mild solutions of second order semilinear impulsive delay integrodifferential equations with nonlocal conditions.Without imposing compactness con...A fixed point analysis approach is used to investigate the existence of mild solutions of second order semilinear impulsive delay integrodifferential equations with nonlocal conditions.Without imposing compactness condition on the cosine family of operators,we give some sufficient conditions for the existence of mild solutions of such system.Finally,an example is presented to illustrate the utility of the proposed result.The results improve some recent results.展开更多
In this paper, we establish sufficient conditions for existence and controllability of nonlinear neutral evolution integroditferential systems in Banach spaces. The result is obtained by using the resolvent operators ...In this paper, we establish sufficient conditions for existence and controllability of nonlinear neutral evolution integroditferential systems in Banach spaces. The result is obtained by using the resolvent operators and fixed point analysis approach.展开更多
Based on the discussion of the semidiscretization of a parabolic equation with asemilinear memory term,an error estimate is derived for the fully discrete scheme with spectral method in space and the backward Euler me...Based on the discussion of the semidiscretization of a parabolic equation with asemilinear memory term,an error estimate is derived for the fully discrete scheme with spectral method in space and the backward Euler method in time The trapezoidal rule is adopted.for the quadrature of the memory term and the quadrature error isestimated.展开更多
In this Paper, we study the existence of solutions for the nonlocal integrodifferential equations with interval impulse and measure of non compactness by using M6nch - fixed point theorem. Finally, an example is given...In this Paper, we study the existence of solutions for the nonlocal integrodifferential equations with interval impulse and measure of non compactness by using M6nch - fixed point theorem. Finally, an example is given to illustrate our main result.展开更多
This work focuses on the existence and trajectory(T-)controllability of mixed fractional Brownian motion(fBm)with the Hurst index(1/2,1)and neutral stochastic integrodifferential equations(NSIDEs)with deviating argume...This work focuses on the existence and trajectory(T-)controllability of mixed fractional Brownian motion(fBm)with the Hurst index(1/2,1)and neutral stochastic integrodifferential equations(NSIDEs)with deviating argument and fBm.Stochastic integrodifferential equations(SIDEs)are solved in Hilbert space using stochastic analysis,the resolvent operator,and Krasnoselskii's fixed point theorem(KFPT).Furthermore,providing adequate assumptions,the T-controllability of the considered system is organised by using extended Gronwall's inequality.We demonstrate the theoretical insights and numerical simulations are included which is unique and makes this work more interesting.The obtained results generalise existing results from[Chalishajar,D.N.,George,R.K.,&Nandakumaran,A.K.(2010).Trajectory controllability of nonlinear integro-differential system.Journal of Franklin Institute,347(7),1065–1075.;Durga,N.,Muthukumar,P.,&Malik,M.(2022).Trajectory controllability of Hilfer fractional neutral stochastic differential equation with deviated argument and mixed fractional Brownian motion.Optimisation,1–27.;Muslim,M.,&George,R.K.(2019).Trajectory controllability of the nonlinear systems governed by fractional differential equations.Differential Equations and Dynamical Systems,27,529–537.;Dhayal,R.,Malik,M.,&Abbas,S.(2021).Approximate and trajectory controllability of fractional stochastic differential equation with non-instantaneous impulses and Poisson jumps.Asian Journal of Control,23(6),2669–2680.].展开更多
In this paper,the approximate controllability of semilinear integrodifferential degenerate Sobolev equations with nonlocal conditions is investigated in the sense of integral solution in Hilbert spaces.Some sufficient...In this paper,the approximate controllability of semilinear integrodifferential degenerate Sobolev equations with nonlocal conditions is investigated in the sense of integral solution in Hilbert spaces.Some sufficient and necessary conditions are obtained.Firstly,the existence and uniqueness of integral solutions of semilinear integrodifferential degenerate Sobolev equations with nonlocal conditions are considered by GE-evolution operator theory and Sadovskii’s fixed point theorem,the existence and uniqueness theorem of solutions is given.Secondly,the approximate controllability of semilinear integrodifferential degenerate Sobolev equations with nonlocal conditions is studied in the sense of integral solution.The criterion for approximate controllability is provided.The obtained results have important theoretical and practical value for the study of controllability of semilinear integrodifferential degenerate Sobolev equations with nonlocal conditions.展开更多
In this paper, the author uses the monotone iterative technique and cone theory to investigate the extremal solutions of two point boundary value problems for nonlinear second order impulsive integrodifferential equa...In this paper, the author uses the monotone iterative technique and cone theory to investigate the extremal solutions of two point boundary value problems for nonlinear second order impulsive integrodifferential equations of mixed type in Banach speces based on a comparison result.展开更多
In this paper, we study operators generated by Volterra-Stieltjes integrodifferential expressions. The selfadjoint boundary conditions are obtained in both regular and limit circle cases. The complete description...In this paper, we study operators generated by Volterra-Stieltjes integrodifferential expressions. The selfadjoint boundary conditions are obtained in both regular and limit circle cases. The complete description of selfadjoint extensions are given.展开更多
We study the periodic boundary value problems for nonlinear integro-differential equa- tions of Volterra type with Carathéodory functions. For two situations relative to lower and upper solutions α and β:αβ ...We study the periodic boundary value problems for nonlinear integro-differential equa- tions of Volterra type with Carathéodory functions. For two situations relative to lower and upper solutions α and β:αβ or β α, the existence of solutions and the monotone iterative method for establishing extreme solutions are considered.展开更多
In this paper we study the higher accuracy methods-the extrapolation and defect correction for the semidiscrete Galerkin approximations to the solutions of hyperbolicintegrodifferential equations. The global extrapola...In this paper we study the higher accuracy methods-the extrapolation and defect correction for the semidiscrete Galerkin approximations to the solutions of hyperbolicintegrodifferential equations. The global extrapolation and the correction approximationsof third order, rather than the pointwise extrapolation results, are derived.展开更多
The authors study an inverse problem for a fractional integrodifferential equation, which aims to determine simultaneously two time varying coefficients, a kernel function and a source function, from the additional in...The authors study an inverse problem for a fractional integrodifferential equation, which aims to determine simultaneously two time varying coefficients, a kernel function and a source function, from the additional integral overdetermination condition. By using the fixed point theorem in suitable Sobolev space, the global existence and uniqueness results of this inverse problem are obtained.展开更多
This paper deals with the uniqueness and existence of periodic solutions of neutral Volterraintegrodifferential equations (1) and (2). Some new unique existence criteria are obtained.
We study the approximate controllability of control systems governed by a class of semilinear integrod- ifferential equations with infinite delays. Sufficient conditions for approximate controllability of semilinear c...We study the approximate controllability of control systems governed by a class of semilinear integrod- ifferential equations with infinite delays. Sufficient conditions for approximate controllability of semilinear control systems are established provided the approximate controllability of the corresponding linear control systems. The results are obtained by using fixed-point theorems and semigroup theory. As an illustration of the application of the approximate controllability results, a simple example is provided.展开更多
In this paper, we discuss the maximum and minimum solutions as will as generalized maximum and minimum solutions of nonlinear integrodifferential equations of mixed type with impulses at fixed moments in Banach soaces...In this paper, we discuss the maximum and minimum solutions as will as generalized maximum and minimum solutions of nonlinear integrodifferential equations of mixed type with impulses at fixed moments in Banach soaces by the theorems of fixed points for inreasing operators.展开更多
文摘This article concerns the construction of approximate solutions for a general stochastic integrodifferential equation which is not explicitly solvable and whose coeffcients functionally depend on Lebesgue integrals and stochastic integrals with respect to martingales. The approximate equations are linear ordinary stochastic differential equations, the solutions of which are defined on sub-intervals of an arbitrary partition of the time interval and connected at successive division points. The closeness of the initial and approximate solutions is measured in the L^p-th norm, uniformly on the time interval. The convergence with probability one is also given.
文摘A nonlinear fractional integrodifferential equation with three-point fractional bound- ary conditions is studied in this paper, and some sufficient conditions for existence and u- niqueness of solutions for the equation are established by Krasnoselskii fixed point theorem and Banach contraction principle, respectively.
文摘Using Daher's fixed point theorem, we obtain a local existence theorem, in which the assumption is weaker than That in the Theorem 2.1 in [2]. Based on this theorem, we get a global existence theorem which is an extension of certain results for ordinary differential equations.
文摘In this Paper. by using the pseudo-spectral method of Fornberg and Whitham, a nonlinear integrodifferential equations is investigated numerically. It is found that for small ∈, the result is close to that of the KdV equation, whereas the effects of larger ∈ and the initial condition are significant.
文摘In this paper, we concertrate our efforts on discuss asymptotic stability of linear inte grodifferential systems with time-varied confficients with large scale via Liapunov functional and decomposite - aggregated method. A group of sufficient conditions are given to guarantee asymptotic stability of zero solutions of systems.
文摘In this paper we prove the existence of mild solutions of a general class of nonlinear evolution integrodifferential equation in Banach spaces. Based on the resolvent operator and the Schaefer fixed point theorem, a sufficient condition for the existence of general integrodifferential evolution equations is established.
基金National Natural Science Foundation of China(No.10971139)
文摘A fixed point analysis approach is used to investigate the existence of mild solutions of second order semilinear impulsive delay integrodifferential equations with nonlocal conditions.Without imposing compactness condition on the cosine family of operators,we give some sufficient conditions for the existence of mild solutions of such system.Finally,an example is presented to illustrate the utility of the proposed result.The results improve some recent results.
文摘In this paper, we establish sufficient conditions for existence and controllability of nonlinear neutral evolution integroditferential systems in Banach spaces. The result is obtained by using the resolvent operators and fixed point analysis approach.
文摘Based on the discussion of the semidiscretization of a parabolic equation with asemilinear memory term,an error estimate is derived for the fully discrete scheme with spectral method in space and the backward Euler method in time The trapezoidal rule is adopted.for the quadrature of the memory term and the quadrature error isestimated.
文摘In this Paper, we study the existence of solutions for the nonlocal integrodifferential equations with interval impulse and measure of non compactness by using M6nch - fixed point theorem. Finally, an example is given to illustrate our main result.
文摘This work focuses on the existence and trajectory(T-)controllability of mixed fractional Brownian motion(fBm)with the Hurst index(1/2,1)and neutral stochastic integrodifferential equations(NSIDEs)with deviating argument and fBm.Stochastic integrodifferential equations(SIDEs)are solved in Hilbert space using stochastic analysis,the resolvent operator,and Krasnoselskii's fixed point theorem(KFPT).Furthermore,providing adequate assumptions,the T-controllability of the considered system is organised by using extended Gronwall's inequality.We demonstrate the theoretical insights and numerical simulations are included which is unique and makes this work more interesting.The obtained results generalise existing results from[Chalishajar,D.N.,George,R.K.,&Nandakumaran,A.K.(2010).Trajectory controllability of nonlinear integro-differential system.Journal of Franklin Institute,347(7),1065–1075.;Durga,N.,Muthukumar,P.,&Malik,M.(2022).Trajectory controllability of Hilfer fractional neutral stochastic differential equation with deviated argument and mixed fractional Brownian motion.Optimisation,1–27.;Muslim,M.,&George,R.K.(2019).Trajectory controllability of the nonlinear systems governed by fractional differential equations.Differential Equations and Dynamical Systems,27,529–537.;Dhayal,R.,Malik,M.,&Abbas,S.(2021).Approximate and trajectory controllability of fractional stochastic differential equation with non-instantaneous impulses and Poisson jumps.Asian Journal of Control,23(6),2669–2680.].
基金supported by the National Natural Science Foundation of China under Grant Nos.12126401 and 11926402。
文摘In this paper,the approximate controllability of semilinear integrodifferential degenerate Sobolev equations with nonlocal conditions is investigated in the sense of integral solution in Hilbert spaces.Some sufficient and necessary conditions are obtained.Firstly,the existence and uniqueness of integral solutions of semilinear integrodifferential degenerate Sobolev equations with nonlocal conditions are considered by GE-evolution operator theory and Sadovskii’s fixed point theorem,the existence and uniqueness theorem of solutions is given.Secondly,the approximate controllability of semilinear integrodifferential degenerate Sobolev equations with nonlocal conditions is studied in the sense of integral solution.The criterion for approximate controllability is provided.The obtained results have important theoretical and practical value for the study of controllability of semilinear integrodifferential degenerate Sobolev equations with nonlocal conditions.
文摘In this paper, the author uses the monotone iterative technique and cone theory to investigate the extremal solutions of two point boundary value problems for nonlinear second order impulsive integrodifferential equations of mixed type in Banach speces based on a comparison result.
文摘In this paper, we study operators generated by Volterra-Stieltjes integrodifferential expressions. The selfadjoint boundary conditions are obtained in both regular and limit circle cases. The complete description of selfadjoint extensions are given.
基金Project supported by the National Natural Science Foundation of China
文摘We study the periodic boundary value problems for nonlinear integro-differential equa- tions of Volterra type with Carathéodory functions. For two situations relative to lower and upper solutions α and β:αβ or β α, the existence of solutions and the monotone iterative method for establishing extreme solutions are considered.
文摘In this paper we study the higher accuracy methods-the extrapolation and defect correction for the semidiscrete Galerkin approximations to the solutions of hyperbolicintegrodifferential equations. The global extrapolation and the correction approximationsof third order, rather than the pointwise extrapolation results, are derived.
基金supported by the National Natural Science Foundation of China(Nos.11201238,11301075)the Jiangsu Provincial Natural Science Foundation of China(No.BK20130594)the Fundamental Research Funds for the Central Universities(No.3207013101)
文摘The authors study an inverse problem for a fractional integrodifferential equation, which aims to determine simultaneously two time varying coefficients, a kernel function and a source function, from the additional integral overdetermination condition. By using the fixed point theorem in suitable Sobolev space, the global existence and uniqueness results of this inverse problem are obtained.
基金project is supported by National Natural Science Foundation of China
文摘This paper deals with the uniqueness and existence of periodic solutions of neutral Volterraintegrodifferential equations (1) and (2). Some new unique existence criteria are obtained.
文摘We study the approximate controllability of control systems governed by a class of semilinear integrod- ifferential equations with infinite delays. Sufficient conditions for approximate controllability of semilinear control systems are established provided the approximate controllability of the corresponding linear control systems. The results are obtained by using fixed-point theorems and semigroup theory. As an illustration of the application of the approximate controllability results, a simple example is provided.
文摘In this paper, we discuss the maximum and minimum solutions as will as generalized maximum and minimum solutions of nonlinear integrodifferential equations of mixed type with impulses at fixed moments in Banach soaces by the theorems of fixed points for inreasing operators.
