EXistence Results for Differential Equations and Inclusions of Arbitrary Order

Abstract

In this thesis, we investigate the existence and uniqueness of solutions for certain boundary value problems generated by fractional differential equations with Caputo derivatives under nonlocal integral boundary conditions, as well as for sequential differential equations with mixed boundary conditions. The results are established us- ing several fixed-point theorems, namely Krasnoselskii’s, Schauder’s, Leray–Schauder, and Banach’s. Furthermore, the study is extended to fractional differential inclusions by employing Krasnoselskii’s fixed-point theorem for multivalued maps and Wegrzyk’sfixed-point theorem.