Functional Integro-differential Equations Research Articles

Neutral Stochastic Integrodifferential Equations Driven by a Fractional Brownian Motion with Impulsive Effects and Time-varying Delays

This paper deals with the existence,uniqueness and asymptotic behaviors of mild solutions to neutral stochastic delay functional integrodifferential equations with impulsive effects, perturbed by a fractional Brownian motion B H , with Hurst parameter \({H \in (\frac{1}{2},1)}\). We use the theory of resolvent operators developed in Grimmer (Trans Am Math Soc 273(1982):333–349, 2009) to show the existence of mild solutions. An example is provided to illustrate the results of this work.

EXITSENCE OF MILD SOLUTIONS FOR SEMILINEAR MIXED VOLTERRA-FREDHOLM FUNCTIONAL INTEGRODIFFERENTIAL EQUATIONS WITH NONLOCALS

Of concern is the existence, uniqueness, and continuous dependence of a mild solution of a nonlocal Cauchy problem for a semilinear mixed Volterra-Fredholm functional integrodifferential equation. Our...

On a new class of impulsive stochastic partial neutral integro-differential equations

In this paper, we introduce a new class of impulsive stochastic partial neutral functional integro-differential equations with infinite delay and not instantaneous impulses in separable Hilbert spaces. We prove the existence of mild solutions for these equations in the -norm without the assumptions of compactness. The results are obtained using suitable fixed point theorems with the properties of analytic resolvent operators. Finally, an example is presented to illustrate the theory.

Maximum Principles for Second-Order Impulsive Integro-Differential Equations with Integral Jump Conditions

We are concerned with two new maximum principles for second-order impulsive integro-differential equations with integral jump conditions. The impulse effects or jump conditions of this paper are involved in terms of integral of past states. As an application, we introduce a new definition of lower and upper solutions which leads to the development of the monotone iterative technique for a periodic boundary value problem related to a nonlinear second-order impulsive functional integro-differential equation with integral jump conditions.

Controllability of nonlocal second-order impulsive neutral stochastic functional integro-differential equations with delay and Poisson jumps

The current paper is concerned with the controllability of nonlocal second-order impulsive neutral stochastic functional integro-differential equations with infinite delay and Poisson jumps in Hilbert spaces. Using the theory of a strongly continuous cosine family of bounded linear operators, stochastic analysis theory and with the help of the Banach fixed point theorem, we derive a new set of sufficient conditions for the controllability of nonlocal second-order impulsive neutral stochastic functional integro-differential equations with infinite delay and Poisson jumps. Finally, an application to the stochastic nonlinear wave equation with infinite delay and Poisson jumps is given.

Square-mean almost automorphic solutions to some stochastic evolution equations I: Autonomous case

This paper concerns the square-mean almost automorphic solutions to a class of abstract semilinear functional integro-differential stochastic evolution equations in real separable Hilbert spaces. Under some suitable assumptions, the existence, uniqueness and asymptotic stability of the square-mean almost automorphic mild solution to some stochastic differential equations are established. As an application, we analyze the almost automorphic mild solution to some stochastic partial functional differential equation which turns out to be in good agreement with our abstract results.

EXISTENCE OF SOLUTIONS FOR NEUTRAL FUNCTIONAL VOLTERRA-FREDHOLM INTEGRODIFFERENTIAL EQUATIONS

In this paper, we study the existence of mild solutions of nonlinear neutral functional VolterraFredholm integrodifferential equations with nonlocal conditions. The results are obtained by using fractional power of operators and Sadovskii’s fixed point theorem.

On Nonlinear Second Order Volterra-Fredholm Functional Integrodifferential Equation with Nonlocal Condition in Banach Spaces

Abstract Our purpose in this paper is to study the existence of solution of nonlinear second order mixed functional integrodifferential equation with nonlocal condition in Banach space by employing two different techniques namely the Darbo-Sadovskii's fixed point theorem with Hausdorff's measure of noncompactness and the Leray Schauder Alternative.

Existence results in the $$\alpha $$ α -norm for neutral partial functional integro-differential equations with infinite delay

In this paper we propose to study, in the \(\alpha \)-norm, a class of neutral partial functional integrodifferential equations with infinite delay. We assume that the linear part generates an analytic and compact semigroup and the nonlinear part of the system involve spatial derivatives. At the end, an example is provided to illustrate the application of the obtained results.

On the asymptotic stability of impulsive neutral stochastic partial integrodifferential equations with variable delays and Poisson jumps

In this work, we study the existence and asymptotic stability in the \(p\)-th moment of mild solutions of nonlinear impulsive stochastic partial functional integrodifferential equations with delays. We suppose that the linear part possesses a resolvent operator in the sense given in Grimmer (Trans. Am. Math. Soc. 273(1), 333–349, 1982) and the nonlinear terms are assumed to be Lipschitz continuous. A fixed point approach is employed for achieving the required result. An example is provided to illustrate the results of this work.

Chelyshkov collocation method for a class of mixed functional integro-differential equations

In this study, a numerical matrix method based on Chelyshkov polynomials is presented to solve the linear functional integro-differential equations with variable coefficients under the initial-boundary conditions. This method transforms the functional equation to a matrix equation by means of collocation points. Also, using the residual function and Mean Value Theorem, an error analysis technique is developed. Some numerical examples are performed to illustrate the accuracy and applicability of the method.

Existence, Regularity and Compactness Properties in the $$\alpha $$ α -Norm for Some Partial Functional Integrodifferential Equations with Finite Delay

In this work, we study in the \(\alpha \)-norm, the existence, the continuity dependence, regularity and compactness of solutions for some partial functional integro-differential equations by using the operator resolvent theory. We suppose that the linear part has a resolvent operator in the sense of Grimmer and Pritchard (J Diff Equ 50:234–259, 1983). The nonlinear part is assumed to be continuous with respect to a fractional power of the linear part in the second variable. An application is provided to illustrate our results.

Existence of Solutions for Neutral Functional Integrodifferential Evolution Equations with Non Local Conditions

We study the existence of mild and strong solutions for nonlinear neutral functional integrodifferential evolution equations with nonlocal conditions in Banach spaces. The results are obtained by using the fractional powers of operators and Sadovskii's fixed point theorem.

Asymptotic stability of neutral stochastic functional integro-differential equations with impulses

This paper is concerned with the existence and asymptotic stability in the \,$p$-th moment ofmild solutions of nonlinear impulsive stochastic delay neutral partial functional integro-differential equations. We suppose that the linear part possesses a resolvent operator in the sense given by Grimmer and the nonlinear terms are assumed to be Lipschitz continuous. A fixed point approach is used to achieve the required result. An example is provided to illustrate the theory developed in this work.

Controllability for some partial functional integrodifferential equations with nonlocal conditions in Banach spaces

Controllability for some partial functional integrodifferential equations with nonlocal conditions in Banach spaces

Existence of mild solutions for impulsive fractional functional integro-differential equations

Existence of mild solutions for impulsive fractional functional integro-differential equations

Existence results in the $$\alpha $$ α -norm for a class of neutral partial functional Integro-differential equations

The goal of this paper is to study, in the \(\alpha \)-norm the existence of solutions for a class of neutral partial functional integrodifferential equations with finite delay. We assume that the linear part generates an analytic and compact semigroup and the nonlinear part is continuous and involves spatial partial derivatives in the second argument. At the end an example is provided to illustrate the application of the obtained results.

Existence and Controllability Results for Mixed Functional Integrodifferential Equations with Infinite Delay

Abstract Sufficient conditions are established for the existence of solution for mixed neutral functional integrodifferential equations with infinite delay. The results are obtained using the theory of fractional powers of operators and the Sadovskii’s fixed point theorem. As an application we prove a controllability result for the system.

Stable solutions of one-leg methods for a class of nonlinear functional-integro-differential equations

This paper deals with stable solutions of one-leg methods for a class of nonlinear functional-integro-differential equations (FIDEs). A type of extended one-leg methods are suggested for the FIDEs. The (weak) global stability results of the methods are presented. In particular, it is shown under suitable condition that a G-stable extended BDF method is globally and asymptotically stable for the problems of class FID(α,β,γ,η,+∞). Numerical experiments further illustrate the theoretical results and the methodical effectiveness. In the end, a connection and comparison between the obtained results and the existed ones is given.

A new operational approach for numerical solution of generalized functional integro-differential equations

In this paper, a class of linear and nonlinear functional integro-differential equations are considered that can be found in the various fields of sciences such as: stress–strain states of materials, motion of rigid bodies and models of polymer crystallization. The operational collocation method with shifted Jacobi polynomial bases is applied to approximate the solution of these equations. In addition, some theoretical results are given to simplify and reduce the computational costs. Finally, some numerical examples are presented to demonstrate the efficiency and accuracy of the proposed method.