Qualitative Study of a Class Fractional Differential Equations and Inclusions in a Banach Space

Abstract

The main goal of this thesis is to present a set of results on the existence and uniqueness of certain classes of the initial value problems and boundary value problems for differential problems involving Caputo, Riemann-Liouville and Hilfer derivatives, under certain conditions. The results have been proven analytically, where the existence results are based on some classical fixed point theorems (Banach, Schaefer, Krasnoselskii) as well as M¨onch’s fixed point theorem combined with the technique of Kuratowski’s measure of noncompactness. To support our results, we provide different illustrative examples in each chapter.