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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