Dynamics of Fractional Delayed Reaction-Diffusion Equations

Linfang Liu; Juan J Nieto

doi:10.3390/e25060950

Dynamics of Fractional Delayed Reaction-Diffusion Equations

Entropy (Basel). 2023 Jun 16;25(6):950. doi: 10.3390/e25060950.

Authors

Linfang Liu¹, Juan J Nieto²

Affiliations

¹ Department of Mathematics, Northwest University, Xi'an 710127, China.
² Departamento de Análise Matemática, Estatística e Optimización, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain.

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

Grants and funding

This research was funded by the Natural Science Foundation of China, grant number 11901448 and 11871022 (Linfang Liu), the Scientific Research Foundation of Northwest University (Linfang Liu), and the Agencia Estatal de Investigación (AEI) of Spain, under Grant PID2020-113275GB-I00, and was co-financed by the European Community Regional Development Fund (FEDER) and by Xunta de Galicia, grant ED431C 2019/02 (Juan J. Nieto). The APC was funded by the Natural Science Foundation of China, grant number 11901448.