On certain boundary value problems involving fractional-order differential equations
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Date
2026
Authors
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Louiza Tabharit / Benali Abdelkader
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.