An existence results for a fractional differential equation with \phi-fractional derivative

Abstract

In this article, we establish certain sufficient conditions to show the existence of solutions of a fractional differential equation with the \phi-Riemann-Liouville and \phi-Caputo fractional derivative in a special Banach space. Our approach is based on fixed point theorems for Meir-Keeler condensing operators via measure of non-compactness. Also an example is given to illustrate our approach.