Initial Value Problem for a Coupled System of Katugampola-Type Fractional Differential Equations

Abstract

The aim of this work is to study the initial value problem of a coupled system of nonlinear fractional differential equations with Katugampola derivative. Some new existence and uniqueness results of solutions for the given problems are obtained by using the Banach contraction principle, Schauder’s and nonlinear alternative Leray–Schauder fixed point theorems. Several examples are presented to illustrate the usefulness of our main results. AMS Subject Classifications: 34A08, 34A12.