WEAK SOLUTION FOR NONLINEAR FRACTIONAL P(.)-LAPLACIAN PROBLEM WITH VARIABLE ORDER VIA ROTHE'S TIME-DISCRETIZATION METHOD

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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Veröffentlicht in:Mathematical modelling and analysis 2022-11, Vol.27 (4), p.533-546
1. Verfasser: Sabri, Abdelali
Format: Artikel
Sprache:eng
Schlagworte:
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
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Zusammenfassung: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.
ISSN:1392-6292
1648-3510
DOI:10.3846/mma.2022.15740