Impulsive Neutral Integro-differential Equations Research Articles

A discussion on boundary controllability of nonlocal impulsive neutral integrodifferential evolution equations

Sufficient conditions for boundary controllability of nonlocal impulsive neutral integrodifferential evolution equations are explored. In the first problem, the outcomes are proven with the help of Sadovskii's fixed point theorem collaborated with strongly continuous semigroup theory. In the second problem, we considered nonautonomous evolution equations, and the result is proven by employing Sadovskii's fixed point theorem in collaboration with the evolution system. Examples are included to demonstrate the theoretical results for both types of equations.

Existence and continuous dependence of mild solutions for impulsive fractional integrodifferential equations in Banach spaces

In the present paper, we investigate the existence, uniqueness, and continuous dependence of mild solutions of impulsive neutral integrodifferential equations with nonlocal conditions in Banach spaces. We use Banach contraction principle and the theory of fractional power of operators to obtain our results. An example is given to illustrate our results.

On Some Results for an Impulsive Neutral Integro-Differential Equations with Deviated Arguments in Banach Spaces

On Some Results for an Impulsive Neutral Integro-Differential Equations with Deviated Arguments in Banach Spaces

Existence results for an impulsive neutral integro-differential equations in Banach spaces

AbstractIn this manuscript we investigate the existence of mild solution for a abstract impulsive neutral integro-differential equation by using semi-group theory and Krasnoselskii-Schaefer fixed point theorem in different approach. At last, an example is also provided to illustrate the obtained results.

Approximate controllability of nonlocal and impulsive neutral integro-differential equations using the resolvent operator theory and an approximating technique

Our purpose in this paper is to study the approximate controllability of nonlocal and impulsive neutral integro-differential equations using the resolvent operator theory, the approximating technique, semigroup theory and the theory of fixed point. We also derive a variation of constants formula for representing a solution of the given system by resolvent operators and then study the existence of a mild solution of the system. We prove the main results by taking the impulsive functions to be continuous only and taking the nonlocal initial condition function to be Lipschitz continuous in the first case and continuous only in the second case. Finally, the main results are illustrated using examples.

Approximate Controllability of Stochastic Fractional Neutral Impulsive Integrodifferential Systems with State Dependent Delay and Poisson Jumps

The purpose of this manuscript is to study the approximate controllability of stochastic fractional impulsive neutral integro-differential equations with state dependent delay and Poisson jumps by using fixed point techniques. By the help of stochastic analysis theory and fractional calculus, we have derived the controllability results. Finally, an example is given to illustrate the obtained abstract result.

Approximate Controllability of impulsive neutral integro-differential equations with deviated arguments and infinite delay in Banach spaces

Approximate Controllability of impulsive neutral integro-differential equations with deviated arguments and infinite delay in Banach spaces

The Impulsive Neutral Integro-Differential Equations with Infinite Delay and Non-Instantaneous Impulses

In this manuscript, we work to accomplish the Krasnoselskii's fixed point theorem to analyze the existence results for an impulsive neutral integro-differential equations with infinite delay and non-instantaneous impulses in Banach spaces. By deploying the fixed point theorem with semigroup theory, we developed the coveted outcomes.

EXISTENCE OF SOLUTIONS FOR IMPULSIVE NEUTRAL FUNCTIONAL INTEGRO DIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS

In this paper, by using fractional power of operators and Sadovskii’s fixed point theorem, we study the existence of mild solution for a certain class of impulsive neutral functional integrodifferential equations with nonlocal conditions. The results we obtained are a generalization and continuation of the recent resultson this issue.

Asymptotic behavior of second-order impulsive partial stochastic functional neutral integrodifferential equations with infinite delay

In this paper, the existence and asymptotic stability in p-th moment of mild solutions to a class of second-order impulsive partial stochastic functional neutral integrodifferential equations with infinite delay in Hilbert spaces is considered. By using H?lder?s inequality, stochastic analysis, fixed point strategy and the theory of strongly continuous cosine families with the Hausdorff measure of noncompactness, a new set of sufficient conditions is formulated which guarantees the asymptotic behavior of the nonlinear second-order stochastic system. These conditions do not require the nonlinear terms are assumed to be Lipschitz continuous. An example is also discussed to illustrate the efficiency of the obtained results.

On existence of solutions of a impulsive stochastic partial functional integro-differential equation with the measure of noncompactness

In this article, we study the existence of mild solutions for a new class of impulsive stochastic partial neutral functional integro-differential equations with infinite delay and non-instantaneous impulses in separable Hilbert spaces. The new results are obtained by using the Hausdorff measure of noncompactness, and the theory of analytic resolvent operators and fractional power of closed operators with the fixed point theorems. An example is also given to illustrate the obtained theory.

Existence and Controllability of Fuzzy Solutions for Impulsive Neutral Functional Integrodifferential Equations

In this paper, the existence, uniqueness and controllability of fuzzy solutions for impulsive neutral functional integrodifferential equations is studied using Banach fixed point theorem.

On Existence of Solutions of Impulsive Nonlinear Functional Neutral Integro-Differential Equations With Nonlocal Condition

AbstractIn the present paper, we investigate the existence, uniqueness and continuous dependence of mild solutions of an impulsive neutral integro-differential equations with nonlocal condition in Banach spaces. We use Banach contraction principle and the theory of fractional power of operators to obtain our results.

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.

Existence results for an impulsive neutral integro-differential equation with infinite delay via fractional operators

In this present work, we consider an impulsive neutral integro-differential equation with infinite delay in an arbitrary Banach space X. The existence of mild solution is established by using resolvent operator and Hausdorff measure of noncompactness.

Robust exponential stability of mild solutions to impulsive stochastic neutral integro-differential equations with delay

Robust exponential stability of mild solutions to impulsive stochastic neutral integro-differential equations with delay

Invariant and attracting sets of non-autonomous impulsive neutral integro-differential equations

This paper is concerned with a non-autonomous impulsive neutral integro-differential equation with time-varying delays. We establish a novel singular delay integro-differential inequality, which enables us to derive several sufficient criteria on the positive invariant set, global attracting set and stability. An example is given to demonstrate the efficiency of proposed r

Solvability for Impulsive Neutral Integro-Differential Equations with State-Dependent Delay via Fractional Operators

This paper is mainly concerned with the existence of mild solutions for a first-order impulsive neutral integro-differential equation with state-dependent delay. We assume that the undelayed part generates an analytic resolvent operator and transforms it into an integral equation. By using a fixed-point theorem for condensing maps combined with theories of analytic resolvent operators, we prove some existence theorems. As an application of these main theorems, some practical consequences are derived.

Exponential stability of nonlinear impulsive neutral integro-differential equations

In this paper, a nonlinear impulsive neutral integro-differential equation with time-varying delays is considered. By establishing a singular impulsive delay integro-differential inequality and transforming the n -dimensional impulsive neutral integro-differential equation to a 2 n -dimensional singular impulsive delay integro-differential equation, some sufficient conditions ensuring the global exponential stability in P C 1 of the zero solution of an impulsive neutral integro-differential equation are obtained. The results extend and improve the earlier publications. An example is also discussed to illustrate the efficiency of the obtained results.

Impulsive Neutral Integrodifferential Equations on Unbounded Intervals

We prove the existence of solutions for a boundary value nonlinear neutral integrodifferential equation with impulsive effects in $$ \mathbb{R}_n $$ defined on an unbounded interval. The result is obtained by using the Schaefer’s fixed point theorem and a recent result on compactness of a continuous operator on the Banach space of bounded continuous functions from a topological space into $$ \mathbb{R}_n $$ .