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
