Fractional Sobolev Spaces With Applications To Boundary Values Problems
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Date
2025-06-15
Journal Title
Journal ISSN
Volume Title
Publisher
Mohamed Boudiaf University of M'sila
Abstract
This thesis aims to study fractional differential equations of both linear and nonlinear
types, based on Riemann–Liouville derivatives of non-integer order.
We begins by presenting the necessary mathematical background, including Lebesgue
and fractional Sobolev spaces, and introduces the fundamental concepts of fractional inte gration and differentiation. These tools are then applied to analyze three main cases of the
studied equation: the sublinear case 1 ≤ q < 2, the superlinear case 2 < q < 2
∗
, and the
linear case q = 2. In each case, we prove the existence of weak solutions within suitable
functional spaces, taking into account the variation of conditions related to the spectral
parameter λ.
Description
Keywords
Riemann–Liouville integral, Riemann–Liouville derivative, fractional Sobolev spaces, fractional boundary value problems