MOHAMEDOURABAH Benmeddour

Bounouiga Mohamed

Etude de quelques équations différentielles et problèmes aux limites liés au calcul fractionnaire conformable

We study the ρ-generalized fractional version of the classical Sturm–Liouville operator. We establish the existence and uniqueness of a boundary value problem for this operator with homogeneous boundary conditions. Using this problem, we present a spectral decomposition of the ρ-generalized fractional Sturm–Liouville operator.

Citation

ABDERACHID Saadi , Mohamedourabah BENMEDDOUR , , (2024-07-20), Spectral decomposition of the fractional Sturm–Liouville operator with ρ -generalized derivative, Applicationes Mathematicae, Vol:51, Issue:1, pages:75-93, Institute of mathematics, polish academic of science

This paper is devoted to the existence and uniqueness of solution to a class of Hadamard fractional differential equation under fractional Sobolev spaces. A novel form of fractional Sobolev space via Hadamard fractional operator is well proposed and related properties are also proved. Furthermore, a variational formulation of considered system is established and thereby the Lax-Milgram theorem is also employed to demonstrate the existence and uniqueness.

Citation

YACINE Arioua , Mohamedourabah BENMEDDOUR , ABDERACHID Saadi , , (2023-03-13), Fractional Sobolev spaces and Boundary Value Problems via Hadamard derivative, Bulletin of the Institute of Mathematics Academia Sinica NEW SERIES, Vol:18, Issue:1, pages:61-83, Bulletin, Institute of Mathematics, Academia Sinica