Applications of Fixed Point Theorems for Coupled Systems of Fractional Integro-Differential Equations Involving Convergent Series

Abstract

The existence and uniqueness of solutions in an appropriate Banach space is established for a coupled system of integro-differential equations involving convergent series, with derivatives of non-integer order on the unknown functions and integrals of Riemann-Liouville in the nonlinearity as well as in the initial conditions. Some illustrative examples are also presented to demonstrate our main results.