Existence and uniqueness of solutions for a nonlinear fractional initial value problem involving Caputo derivatives

Abstract

In this paper, we give a sufficient condition for the existence and uniqueness interval of continuous solutions to a class of fractional initial value problems involving Caputo derivatives when the data functions satisfy a non-classical Lipschitz condition. The main tool used in the paper is a fixed point theorem for generalized contractions due to Browder-Matkowski.