Weak solution for nonlinear fractional p(.)-Laplacian problem with variable order via Rothe's time-discretization method

In this paper, we prove the existence and uniqueness results of weak solutions to a class of nonlinear fractional parabolic p(.)-Laplacian problem with variable order. The main tool used here is the Rothe’s method combined with the theory of variable-order fractional Sobolev spaces with variable exp...

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Bibliographic Details
Published inMathematical modelling and analysis Vol. 27; no. 4; pp. 533 - 546
Main Author Sabri, Abdelali
Format Journal Article
LanguageEnglish
Published Vilnius Vilnius Gediminas Technical University 10.11.2022
Subjects
Banach spaces
fractional p(.)-Laplacian
fractional Sobolev space
Laplacian operator
Mathematical research
Partial differential equations
Rothe’s method
semi-discretization
Sobolev space
Topological spaces
variable exponent
variable order
Morocco
semi-discretization
weak solution
fractional p(.)-Laplacian
variable exponent
variable order
fractional Sobolev space
Rothe’s method
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Summary:In this paper, we prove the existence and uniqueness results of weak solutions to a class of nonlinear fractional parabolic p(.)-Laplacian problem with variable order. The main tool used here is the Rothe’s method combined with the theory of variable-order fractional Sobolev spaces with variable exponent.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1392-6292
1648-3510
DOI:10.3846/mma.2022.15740