Existence and Uniqueness Results of Coupled Fractional-Order Differential Systems Involving Riemann–Liouville Derivative in the Space Wa+γ1,1(a,b)×Wa+γ2,1(a,b) with Perov’s Fixed Point Theorem

Abstract

This paper is devoted to studying the existence and uniqueness of a system of coupled fractional differential equations involving a Riemann–Liouville derivative in the Cartesian product of fractional Sobolev spaces E=Wa+γ1,1(a,b)×Wa+γ2,1(a,b). Our strategy is to endow the space E with a vector-valued norm and apply the Perov fixed point theorem. An example is given to show the usefulness of our main results.