Asymptotic Behavior of Delayed Reaction-Diffusion Neural Networks Modeled by Generalized Proportional Caputo Fractional Partial Differential Equations

Fractal and Fractional

article

Ravi P. Agarwal¹  Snezhana Hristova²  Donal O’Regan³ 

[1] Department of Mathematics, Texas A&M University-Kingsville;Faculty of Mathematics and Informatics, Plovdiv University “P. Hilendarski”;School of Mathematical and Statistical Sciences, University of Galway

关键词: reaction-diffusion neural networks;    generalized proportional Caputo fractional derivatives;    delays;    asymptotic behavior;   

DOI  :  10.3390/fractalfract7010080

学科分类：社会科学、人文和艺术（综合）

来源: mdpi

【 摘 要 】

In this paper, a delayed reaction-diffusion neural network model of fractional order and with several constant delays is considered. Generalized proportional Caputo fractional derivatives with respect to the time variable are applied, and this type of derivative generalizes several known types in the literature for fractional derivatives such as the Caputo fractional derivative. Thus, the obtained results additionally generalize some known models in the literature. The long term behavior of the solution of the model when the time is increasing without a bound is studied and sufficient conditions for approaching zero are obtained. Lyapunov functions defined as a sum of squares with their generalized proportional Caputo fractional derivatives are applied and a comparison result for a scalar linear generalized proportional Caputo fractional differential equation with several constant delays is presented. Lyapunov functions and the comparison principle are then combined to establish our main results.

【 授权许可】

CC BY