Fractional Sobolev spaces and Boundary Value Problems via Hadamard derivative
by M. O. Benmeddour   A. Saadi   Y. Arioua  

Vol. 18 No. 1 (2023) P.61~P.83

DOI:	https://doi.org/10.21915/BIMAS.2023104
	10.21915/BIMAS.2023104

ABSTRACT

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.

KEYWORDS
Fractional derivative, Boundary value problem, Hadamard

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 26A33, 34A08, 34Bxx

MILESTONES

Received: 2022-11-14
Revised :
Accepted:

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