Caputo–Hadamard fractional differential Cauchy problem in Fréchet spaces

Abstract

This article deals with some existence results of solutions for a class of differential equations involving the Caputo–Hadamard fractional derivative in Frechet spaces. These results are based on a generalization of the classical Darbo fixed point theorem for Frechet spaces associated with the concept of measure of noncompactness. We illustrate our results by an example.