New results for a system of two fractional differential equations involving n Caputo derivatives

Abstract

This paper studies a coupled system of two differential equations of arbitrary orders using Caputo approach with n derivatives, n ∈ N ∗ , n 6 = 1. New existence and uniqueness results are established using Banach contraction principle. Other existence results are obtained using Schaefer and Krasnoselskii fixed point theorems. Some illustrative examples are also presented.