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Unique solvability of a Dirichlet problem for a fractional parabolic equation using energy-inequality method


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.


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Article Information

TitleUnique solvability of a Dirichlet problem for a fractional parabolic equation using energy-inequality method
SourceMethods Funct. Anal. Topology, Vol. 26 (2020), no. 3, 216-226
DOI10.31392/MFAT-npu26_3.2020.03
MilestonesReceived 06/01/2020; Revised 04/08/2020
CopyrightThe 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


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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},
       DOI = {10.31392/MFAT-npu26_3.2020.03},
       URL = {http://mfat.imath.kiev.ua/article/?id=1394},
}


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