Existence of Mild Solutions for Impulsive Fractional Integro-Differential Inclusions with State-Dependent Delay

Abstract

Abstract:In this manuscript, we implement Bohnenblust-Karlin's fixed point theorem to demonstrate the existence of mild solutions for a class of impulsive fractional integro-differential inclusions (IFIDI) with state-dependent delay (SDD) in Banach spaces. An example is provided to illustrate the obtained abstract results.

On mild solutions for integrodifferential systems with integral impulses in Banach spaces

“…The theory of impulsive equattions has been widely developed, especially concerning differential equations (see for example the papers of Wang and Ezzinbi [20], Mophou [18], Suganya and Arjunan [19], Hernandez et al [15], Chadha and Pandey [8] and the book of Benchora et al [3]).…”

Solutions for impulsive fractional pantograph differential equation via generalized anti-periodic boundary condition

“…The main aim of this paper is to establish the existence and uniqueness of solutions for the boundary value problem (1.3), by using the contraction principle of Banach and the fixed point theorem of Krasnoselskii. Presently, different techniques have been extensively applied in obtaining solutions to the impulsive fractional differential equations (see, e.g., [20,41,44]). However, in this article, we adopt the solution approach used in [47] to solve the impulsive fractional equation (13).…”

Existence of solutions for nonlocal boundary value problem for Caputo nonlinear fractional differential inclusion

“…Realistic problems arising from economics, optimal control, stochastic analysis can be modelled as differential inclusion. So much attention has been paid by many authors to study this kind of problems, see [4,5,36]. On the other hand boundary value problems with local and nonlocal boundary conditions constitute a very interesting and important class of problems.…”