Study of a Coupled System of Integro-Differential Equations Involving the Generalized Proportional Caputo Derivatives

This paper deals with a new coupled system of integro-differential equations involving the generalized proportional Caputo derivatives equipped with nonlocal four-point boundary conditions. Sufficient criteria for the existence and uniqueness of solutions for the studied system are derived based on Krasnoselskii’s and Banach fixed-point theorems, respectively. Applications are constructed with three different cases to illustrate the main results.