Functional Integro-differential Equations Research Articles

Mild solution of neutral stochastic partial functional integrodifferential equations with non-Lipschitz coefficients

The article presents the results on existence and uniqueness of mild solutions to some neutral stochastic partial differential equations under Caratheodory-type conditions. The results are obtained by using the method of Picard approximation and generalize the results that were reported by Bao and Hou (Comput Math Appl 59:207–214, 2010). The theory of resolvent operators developed by Grimmer (Trans Am Math Soc 273:333–349, 1982) is employed to demonstrate the existence of mild solutions. A pratical example is provided to illustrate the abstract results of this work.

Nonlinear boundary value problems of fractional functional integro-differential equations

In this paper, we consider the existence of generalized solutions for fractional functional integro-differential equations of mixed type with nonlinear boundary value conditions. By establishing a new comparison theorem and applying the monotone iterative technique, we show the existence of extremal generalized solutions.

Global existence for abstract nonlinear Volterra–Fredholm functional integrodifferential equation

Abstract In the present paper, we investigate the global existence of solutions to initial value problem for nonlinear mixed Volterra–Fredholm functional integrodifferential equations in Banach spaces. The technique used in our analysis is based on an application of the topological transversality theorem known as Leray–Schauder alternative and rely on a priori bounds of solution.

Numerical Solution of Functional Integral and Integro-Differential Equations by Using B-Splines

This paper describes an approximating solution, based on Lagrange interpolation and spline functions, to treat functional integral equations of Fredholm type and Volterra type. This method extended to functional integral and integro-differential equations. For showing efficiency of the method we give some numerical examples.

Existence and Uniqueness of Mild Solutions to Some Neutral Stochastic Partial Functional Integrodifferential Equations with Non-Lipschitz Coefficients

This paper presents the result on existence, uniqueness of mild solutions to neutral stochastic partial functional integrodifferential equations under the Carathéodory-type conditions on the coefficients. The results are obtained by using the method of successive approximation. An example is provided to illustrate the results of this work.

A Global Existence and Uniqueness Result for Functional Integro-Differential Equations in Banach Spaces

We provide in this paper, sufficient conditions for the existence of the unique mild solution on the semi-infinite interval for fractional integro-differential equa- tions with time delay by using a recent nonlinear alternative of Leray-Schauder type due to Frigon and Granas for contractions maps in Frechet spaces. Mathematics Subject Classication 2000: 26A33, 45J05, 45G05, 34A08, 34K37.

Regularity for Variational Evolution Integrodifferential Inequalities

We deal with the regularity for solutions of nonlinear functional integrodifferential equations governed by the variational inequality in a Hilbert space. Moreover, by using the simplest definition of interpolation spaces and the known regularity result, we also prove that the solution mapping from the set of initial and forcing data to the state space of solutions is continuous, which very often arises in application. Finally, an example is also given to illustrate our main result.

Integral boundary value problems for first order nonlinear impulsive functional integro-differential differential equations

In this paper, we consider the existence of solutions for first order nonlinear impulsive functional integro-differential equations with integral boundary value conditions. We firstly build a new comparison theorem. Then by utilizing the monotone iterative technique and the method of lower and upper solutions, we obtain the existence of extremal solutions or quasi-solutions.

Asymptotic behavior of solutions of some semilinear functional differential and integro-differential equations with infinite delay in Banach spaces

We prove in this paper the existence and uniqueness of mild solutions to some functional differential and functional integro-differential equations with infinite delay in Banach spaces which approach almost automorphic functions at infinity. We also discuss the existence of S-asymptotically ω - periodic mild solutions. The results are new.

CONTROLLABILITY OF STOCHASTIC FUNCTIONAL INTEGRODIFFERENTIAL EVOLUTION SYSTEMS

In this paper, we prove the existence and uniqueness of mild solution for stochastic functional integrodifferential evolution equations and derive sufficient conditions for the controllability results. As an illustration we consider the controllability for a system governed by a random motion of a string.

New Existence Results and Comparison Principles for Impulsive Integral Boundary Value Problem with Lower and Upper Solutions in Reversed Order

This paper investigates the existence of the extremal solutions to the integral boundary value problem for first-order impulsive functional integrodifferential equations with deviating arguments under the assumption of existing upper and lower solutions in the reversed order. The sufficient conditions for the existence of solutions were obtained by establishing several new comparison principles and using the monotone iterative technique. At last, a concrete example is presented and solved to illustrate the obtained results.

Boundary value problem for first order impulsive functional integro-differential equations

This paper investigates extremal solutions of the boundary value problem for impulsive functional integro-differential equations with nonlinear boundary conditions and deviating arguments. In the presence of a lower solution u and an upper solution v with u ≥ v , existence of extremal solutions is proved by establishing a new comparison principle and using the monotone iterative technique.

Existence of solutions for nonlocal impulsive partial functional integrodifferential equations via fractional operators

In this paper, by using the Leray–Schauder alternative, we have investigated the existence of mild solutions to first-order impulsive partial functional integrodifferential equations with nonlocal conditions in an α -norm. We assume that the linear part generates an analytic compact bounded semigroup, and that the nonlinear part is a Lipschitz continuous function with respect to the fractional power norm of the linear part. An example is also given to illustrate our main results.

Existence of solutions for neutral functional integrodifferential equations

In this paper, by using fractional power of operators and Sadovskii's fixed point theorem, we study the existence of mild and strong solutions of nonlinear neutral functional integrodifferential equations. The results we obtained are a generalization and continuation of the recent results on this issue.

Existence of solutions for nonlinear functional integrodifferential evolution equations with nonlocal conditions

In this paper, we prove the existence of mild solutions for nonlinear functional integrodifferential evolution equations with nonlocal conditions in Banach spaces. The results are obtained by using the theory of resolvent operators and Leray–Schauder nonlinear alternative.

Existence results for neutral functional integrodifferential equations with infinite delay via fractional operators

This paper is concerned with the existence of mild solutions for partial neutral functional integrodifferential equations with infinite delay in a Banach space. The results are obtained by using the resolvent operators and Krasnoselski-Schaefer type fixed point theorem. An example is given to illustrate the results.

On state-dependent delay partial neutral functional integro–differential equations

In this paper the existence of mild solutions for a class of abstract neutral integro–differential equations with state-dependent delay is studied.

Existence results for fractional functional integrodifferential equations with nonlocal conditions in Banach spaces

The paper establishes a sufficient condition for the existence of mild solutions of fractional functional integrodifferential equations with nonlocal conditions in Banach spaces. Our approach is based on Schaefer's fixed point theorem combined with the us

EXACT NULL CONTROLLABILITY OF ABSTRACT SEMILINEAR FUNCTIONAL INTEGRODIFFERENTIAL STOCHASTIC EVOLUTION EQUATIONS IN HILBERT SPACES

Sufficient conditions for exact null controllability of the semilinear integrodifferential stochastic evolution equations in Hilbert space are obtained. It is shown that the exact null controllability of the corresponding linear system with additive term implies the exact null controllability of the semilinear functional integrodifferential stochastic evolution equations. An application to stochastic partial integrodifferential equations is given.

On Solution of a Nonlinear Functional Integrodifferential Equations with Nonlocal Conditions in Banach Spaces

In paper is concerned with a class of first-order nonlinear functional integrodifferential equations with nonlocal conditions in Banach spaces. Sufficient conditions for existence of mild solutions are obtained by using the theory of resolvent operators, Banach’s contraction principle and Schaefer’s fixed point theorem. As an application, we also consider a partial functional integrodifferential equation.