Global existence and large time behavior of solutions of a time fractional reaction diffusion system

Ahmed Alsaedi; Bashir Ahmad; Mokhtar Kirane; Rafika Lassoued

doi:10.1515/fca-2020-0019

Global existence and large time behavior of solutions of a time fractional reaction diffusion system

Ahmed Alsaedi, Bashir Ahmad, Mokhtar Kirane, Rafika Lassoued

Mathematics

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4 Scopus citations

Abstract

In this paper, it is proved that a time fractional reaction diffusion system with reaction terms of the Brusselator type admits a global solution by using the feedback method of F. Rothe [20]. Furthermore, some results on the large time behavior of the solutions are obtained. We give a positive answer to Problem 6 of the valuable paper of Gal and Warma [6].

Original language	British English
Pages (from-to)	390-407
Number of pages	18
Journal	Fractional Calculus and Applied Analysis
Volume	23
Issue number	2
DOIs	https://doi.org/10.1515/fca-2020-0019
State	Published - 1 Apr 2020

Keywords

Caputo derivative
fractional calculus
large time behavior
local and global existence
reaction-diffusion system

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abstract = "In this paper, it is proved that a time fractional reaction diffusion system with reaction terms of the Brusselator type admits a global solution by using the feedback method of F. Rothe [20]. Furthermore, some results on the large time behavior of the solutions are obtained. We give a positive answer to Problem 6 of the valuable paper of Gal and Warma [6].",

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AU - Ahmad, Bashir

AU - Kirane, Mokhtar

AU - Lassoued, Rafika

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N2 - In this paper, it is proved that a time fractional reaction diffusion system with reaction terms of the Brusselator type admits a global solution by using the feedback method of F. Rothe [20]. Furthermore, some results on the large time behavior of the solutions are obtained. We give a positive answer to Problem 6 of the valuable paper of Gal and Warma [6].

AB - In this paper, it is proved that a time fractional reaction diffusion system with reaction terms of the Brusselator type admits a global solution by using the feedback method of F. Rothe [20]. Furthermore, some results on the large time behavior of the solutions are obtained. We give a positive answer to Problem 6 of the valuable paper of Gal and Warma [6].

KW - Caputo derivative

KW - fractional calculus

KW - large time behavior

KW - local and global existence

KW - reaction-diffusion system

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IS - 2

ER -

Global existence and large time behavior of solutions of a time fractional reaction diffusion system

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Keywords

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