New results on Caputo fractional Volterra-Fredholm integro-differential equations with nonlocal conditions

Abstract

This article investigates the existence and uniqueness of solutions for a nonlocal initial condition of the Caputo fractional Volterra-Fredholm integro-differential equation in a Banach space. We shall prove the existence and uniqueness of the results by using the Banach and Krasnoselskii fixed-point theorems. A number of illustrative examples will be given to further the understanding of our main conclusions.