Existence results for coupled differential equations of non-integer order with riemann-liouville, erdélyi-kober integral conditions

Abstract

This paper proposes the existence and uniqueness of a solution for a coupled system that has fractional differential equations through Erdélyi-Kober and Riemann-Liouville fractional integral boundary conditions. The existence of the solution for the coupled system by adopting the Leray-Schauder alternative. The uniqueness of solution for the problem can be found using Banach fixed point theorem. In order to verify the proposed criterion, some numerical examples are also discussed. © 2021 the Author(s), licensee AIMS Press.