On the Existence of \chi-Differentiable Solutions for Sequential Differential System Involving a Mixed Derivative in Banach space

Abstract

In this article, we aim to study the existence of -continuously differentiable solutions for an integral boundary value problem to sequential differential system involving a mixed derivative in Banach space. We apply the Mönch fixed point theorem combined with the Kuratowski measure of noncompactness to obtain this result. We also obtain the compactness of the solution set for the given problem, an example is given to illustrate the results obtained.