Electron. J. Diff. Equ., Vol. 2014 (2014), No. 179, pp. 1-10.

Existence and uniqueness of solutions to parabolic fractional differential equations with integral conditions

Taki-Eddine Oussaeif, Abdelfatah Bouziani

In this article, we establish sufficient conditions for the existence and uniqueness of a solution, in a functional weighted Sobolev space, for partial fractional differential equations with integral conditions. The results are established by applying the energy inequality method, and the density of the range of the operator generated by the problem.

Submitted June 11, 2014. Published August 25, 2014.
Math Subject Classifications: 35D05, 35K15, 35K20, 35B45, 35A05.
Key Words: Partial fractional differential equation; energy inequality; integral condition; existence; uniqueness.

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Taki-Eddine Oussaeif
Department of Mathematics and Informatics
The Larbi Ben M'hidi University, Oum El Bouaghi, Algeria
email: taki_maths@live.fr
Abdelfatah Bouziani
Departement de Mathematiques et Informatique
Universite Larbi Ben M'hidi-Oum El Bouagui 04000, Algeria
email: af_bouziani@hotmail.com

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