On certain boundary value problems involving fractional-order differential equations

Abstract

This thesis presents several results on the existence, uniqueness, and stability of nonlocal and boundary value problems for differential equations involving the generalized Caputo fractional derivatives. In addition, we investigate coupled systems of nonlinear fractional differential equations within the same framework. The analysis relies on fixed point theorems, including those of Krasnoselskii, Dhage, Schaefer, and the Banach contraction principle. Moreover, the study extends to Banach spaces, employing Darbo’s fixed-point theorem in conjunction with the measure of noncompactness technique. Each chapter is considered a continuation of the previous one and ends with illustrations to show the applicability of the results.