Impulsive Functional Integrodifferential Equations Research Articles

Controllability result in α-norm for some impulsive partial functional integrodifferential equation with infinite delay in Banach spaces

Abstract The purpose of this paper is to study the controllability in the α-norm for some impulsive partial functional integrodifferential equation with infinite delay in Banach space. To do this, we give sufficient conditions ensuring the controllability by assuming that the undelayed part admits a resolvent operator in the sense of Grimmer and that the delayed part is continuous with respect to the fractional power of the generator. The results are obtained by using the Schauder fixed-point theorem.

Results on nonlocal controllability for impulsive fractional functional integro-differential equations via degree theory

This manuscript mainly focuses on the nonlocal controllability analysis for the impulsive fractional functional integro-differential equation (IFrFIDE) in n-dimensional Euclidean space. To attain the solution representation of the given system, we use the Laplace transform technique and the Mittag-Leffler function. Initially, we obtained the existence and uniqueness of a solution by using the topological degree method, contraction mapping and Gronwall’s inequality. Moreover, we also explore the nonlocal controllability results for our given problem. Furthermore, two numerical examples and a filter system are provided for our given dynamical system. It is helpful to demonstrate the efficacy of our findings.

Controllability of neutral impulsive stochastic functional integrodifferential equations driven by a fractional Brownian motion with infinite delay via resolvent operator

This paper is concerned with the controllability results of neutral impulsive stochastic functional integrodifferential equations driven by a fractional Brownian motion with infinite delay in a real separable Hilbert space. The controllability results are obtained using stochastic analysis, the theory of resolvent operator in the sense of Grimmer and Krasnoselskii fixed point theorem. An example is provided to illustrate the obtained theory.

Controllability of impulsive stochastic functional integrodifferential equations driven by Rosenblatt process and Lévy noise

In this paper, we develop controllability findings for impulsive neutral stochastic delay partial integrodifferential equations in Hilbert spaces driven by Rosenblatt process and Lévy noise. A novel set of adequate requirements is obtained by utilizing a fixed point method without imposing a stringent compactness constraint on the semigroup. The observed results represent a generalization and continuation of previous findings on this topic. Finally, an example is given to demonstrate how the acquired findings may be used.

Existence and Hyers-Ulam stability of random impulsive stochastic functional integrodifferential equations with finite delays

In this article, we concentrate on the existence and Hyers-Ulam stability of random impulsive stochastic functional integrodifferential equations with finite delays. Initially, the existence of the mild solutions to the equations by utilizing Banach fixed point theorem is demonstrated. In the later case we explore the Hyers Ulam stability results under the Lipschitz condition on a bounded and closed interval.

Asymptotic properties of solutions for impulsive neutral stochastic functional integro-differential equations

In this work, we are concerned with the asymptotic properties of solutions for an impulsive neutral stochastic functional integro-differential equation. By applying the theory of resolvent operators, the Banach fixed point principle theorem, and results on stochastic analysis, we study respectively the existence, uniqueness, and global attracting and quasi-invariant sets of mild solutions for the considered equation. We also derive some sufficient conditions of pth moment exponential stability and almost surely exponential stability of the mild solutions. An example is provided in the end to illustrate the applications of the obtained results.

Controllability for some nonlinear impulsive partial functional integrodifferential systems with infinite delay in Banach spaces

This work concerns the study of the controllability for some impulsive partial functional integrodifferential equation with infinite delay in Banach spaces. We give sufficient conditions that ensure the controllability of the system by supposing that its undelayed part admits a resolvent operator in the sense of Grimmer, and by making use of the measure of noncompactness and the Mönch fixed-point Theorem. As a result, we obtain a generalization of the work of K. Balachandran and R. Sakthivel (Journal of Mathematical Analysis and Applications, 255, 447-457, (2001)) and a host of important results in the literature, without assuming the compactness of the resolvent operator. An example is given for illustration.

Stability for some impulsive neutral stochastic functional integro-differential equations driven by fractional Brownian motion

The aim of this work is to study the stability for some integro-differential equations with impulses driven by fractional Brownian motion with noncompact semigroup in Hilbert spaces. We assume that...

Existence and Stability Results for Impulsive Stochastic Functional Integrodifferential Equation with Poisson Jumps

In this article we present the existence, uniqueness and stability of mild solutions for impulsive stochastic functional integro differential equations with non-Lipschitz condition. The mild solution is obtained by using a resolvent operator in a different sense and the results are proved by using the method of successive approximation and Bihari’s inequality.

Optimal Solutions of Fractional Nonlinear Impulsive Neutral Stochastic Functional Integro-Differential Equations

In this article, we consider a new class of fractional impulsive neutral stochastic functional integro-differential equations with infinite delay in Hilbert spaces. First, by using stochastic analysis, fractional calculus, analytic α-resolvent operator and suitable fixed point theorems, we prove the existence of mild solutions and optimal mild solutions for these equations. Second, the existence of optimal pairs of system governed by fractional impulsive partial stochastic integro-differential equations is also presented. The results are obtained under weaker conditions in the sense of the fractional power arguments. Finally, an example is given for demonstration.

Existence of Fractional Impulsive Functional Integro-Differential Equations in Banach Spaces

In this paper, we establish the existence of piece wise (PC)-mild solutions (defined in Section 2) for non local fractional impulsive functional integro-differential equations with finite delay. The proofs are obtained using techniques of fixed point theorems, semi-group theory and generalized Bellman inequality. In this paper, we used the distributed characteristic operators to define a mild solution of the system. We also discussed the controversy related to the solution operator for the fractional order system using weak and strong Caputo derivatives. Examples are given to illustrate the theory.

ON THE CONTROLLABILITY OF IMPULSIVE FUNCTIONAL INTEGRO-DIFFERENTIAL EQUATIONS IN BANACH SPACES

In this paper, we established the some sufficient conditions for controllability of impulsive functional integrodifferential equations with nonlocal conditions by using the measure of noncompactness and Monch fixed point theorem.

A new comparison principle and its application to nonlinear impulsive functional integro-differential equations

In this article, we first create a new comparison principle for a nonlinear impulsive boundary problem involving different deviating arguments. Then we employ the new result and iterative method to study the existence of the max-minimal solution of a second-order impulsive functional integro-differential equation. The results achieved in this paper are more general and complement many previously known results.

Approximate Controllability Results for Impulsive Partial Functional Nonlocal Integro-differential Evolution Systems through Resolvent Operators

This paper investigates the existence and approximate controllability results for a class of impulsive functional integro-differential evolution systems with nonlocal conditions via resolvent operators in Banach spaces. By making utilization of Banach contraction principle and Schaefer’s fixed point theorem along with resolvent operators and semigroup theory, we build up the desired results. As an application, we also consider an impulsive partial functional integro-differential equations.

Existence of Optimal Mild Solutions for Multi-valued Impulsive Stochastic Partial Functional Integrodifferential Equations

In this paper, we introduce a new class of multi-valued impulsive stochastic partial functional integrodifferential equations with infinite delay in the $$\alpha $$ -norm. Using stochastic analysis, analytic semigroup and fixed point strategy with the properties of fractional powers of closed operators, we establish the existence and uniqueness results of mild solutions for these equations with not instantaneous impulse. Then, the existence of optimal mild solutions is also proved. Particularly, the compactness of the operator semigroups is not needed. Finally, an example to illustrate the applications of main results is given.

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.

Impulsive hybrid interval-valued functional integro-differential equations

Impulsive hybrid interval-valued functional integro-differential equations

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.

NONLOCAL CONTROLLABILITY OF IMPULSIVE FUNCTIONAL INTEGRO-DIFFERENTIAL EQUATIONS IN BANACH SPACES

The paper is concerned with the controllability of impulsive functional integrodifferential equations with nonlocal conditions. Using the measure of noncompactness and Monch fixed point theorem, we establish some sufficient conditions for controllability and also our theorems extend some analogous results of (impulsive) control systems.

Local and global existence of mild solution to impulsive fractional semilinear integro-differential equation with noncompact semigroup

In this paper, we study local and global existence of mild solution for an impulsive fractional functional integro differential equation with non-compact semi-group in Banach spaces. We establish a general framework to find the mild solutions for impulsive fractional integro-differential equations, which will provide an effective way to deal with such problems. The theorems proved in this paper improve and extend some related conclusions on this topic. Finally, two applications are given to illustrate that our results are valuable.