Abstract
In this paper, we establish sufficient conditions for the existence and
uniqueness of the solution in fractional functional space for a class of
initial boundary-value problems for a class of partial fractional parabolic
differential equations that include a fractional derivative of Caputo. The
results are established by the application of the method based on a priori
estimate "energy inequality" and the density of the range of the operator
generated by the problem considered.
Встановлені достатні умови існування та єдиності розв'язку з
дробового функціонального простору для одного класу початково-крайових
задач для деяких дробово-параболічних диференціальних рівнянь із
дробовою похідною Капуто. Результати отримано шляхом застосування
методу енергетичних нерівностей. Доведена щільність образу оператора,
що відповідає задачі.
Key words: Partial fractional differential equation, energy inequality,
existence, uniqueness.
Full Text
Article Information
| Title | Unique solvability of a Dirichlet problem for a fractional parabolic equation using energy-inequality method |
| Source | Methods Funct. Anal. Topology, Vol. 26 (2020), no. 3, 216-226 |
| DOI | 10.31392/MFAT-npu26_3.2020.03 |
| MathSciNet |
MR4165153 |
| Milestones | Received 06/01/2020; Revised 04/08/2020 |
| Copyright | The Author(s) 2020 (CC BY-SA) |
Authors Information
Benaoua Antara
Department of Mathematics and Informatics. The Larbi Ben M'hidi University, Oum El Bouaghi; Dynamic and control systems laboratory; Oum El Bouaghi University
Oussaeif Taki-Eddine
Department of Mathematics and Informatics. The Larbi Ben M'hidi University, Oum El Bouaghi
Rezzoug Imad
Department of Mathematics and Informatics. The Larbi Ben M'hidi University, Oum El Bouaghi
Citation Example
Benaoua Antara, Oussaeif Taki-Eddine, and Rezzoug Imad, Unique solvability of a Dirichlet problem for a fractional parabolic equation using energy-inequality method, Methods Funct. Anal. Topology 26
(2020), no. 3, 216-226.
BibTex
@article {MFAT1394,
AUTHOR = {Benaoua Antara and Oussaeif Taki-Eddine and Rezzoug Imad},
TITLE = {Unique solvability of a Dirichlet problem for a fractional parabolic equation using energy-inequality method},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {26},
YEAR = {2020},
NUMBER = {3},
PAGES = {216-226},
ISSN = {1029-3531},
MRNUMBER = {MR4165153},
DOI = {10.31392/MFAT-npu26_3.2020.03},
URL = {http://mfat.imath.kiev.ua/article/?id=1394},
}
