Dynamics of Fractional Delayed Reaction-Diffusion Equations

Liu, Linfang; Nieto, Juan J.

doi:10.3390/e25060950

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Article

16 June 2023

15 Pages

Dynamics of Fractional Delayed Reaction-Diffusion Equations

and

Department of Mathematics, Northwest University, Xi’an 710127, China

Departamento de Análise Matemática, Estatística e Optimización, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain

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Entropy2023, 25(6), 950;https://doi.org/10.3390/e25060950

This article belongs to the Special Issue Selected Papers from the 2022 Scholars International Conference on Physics and Quantum Physics

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Abstract

The long-term behavior of the weak solution of a fractional delayed reaction–diffusion equation with a generalized Caputo derivative is investigated. By using the classic Galerkin approximation method and comparison principal, the existence and uniqueness of the solution is proved in the sense of weak solution. In addition, the global attracting set of the considered system is obtained, with the help of the Sobolev embedding theorem and Halanay inequality.

Keywords:

fractional reaction–diffusion equations; bounded variable delay; generalized fractional derivative; generalized comparison principal; global attracting sets

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