On Riesz-Caputo Fractional Differential Problems via Fixed Point Theory and Measure of Noncompactness

Abstract

This article deals with the existence and stability results for a class of initial value problems involving the Riesz-Caputo fractional derivative. In this paper, we will study two types of fractional differential problem, the result of the first one is based on Schaefer's fixed point theorem. The same problem but in Banach spaces is investigated using Sadovskii's fixed point theorem. The third problem is an implicit problem with retarded and advanced arguments, the results are based on Sadovskii's fixed point theorem combined with the technique of measure of noncompactness. Some examples are given to validate our main results.