Asymptotic Behavior of Delayed Reaction-Diffusion Neural Networks Modeled by Generalized Proportional Caputo Fractional Partial Differential Equations
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 th...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-01-01
|
| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/7/1/80 |
| _version_ | 1797442339588800512 |
|---|---|
| author | Ravi P. Agarwal Snezhana Hristova Donal O’Regan |
| author_facet | Ravi P. Agarwal Snezhana Hristova Donal O’Regan |
| author_sort | Ravi P. Agarwal |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T12:40:24Z |
| format | Article |
| id | doaj.art-fe426fbc3109467cb5fa2699bbf2cafb |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T12:40:24Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-fe426fbc3109467cb5fa2699bbf2cafb2023-11-30T22:20:03ZengMDPI AGFractal and Fractional2504-31102023-01-01718010.3390/fractalfract7010080Asymptotic Behavior of Delayed Reaction-Diffusion Neural Networks Modeled by Generalized Proportional Caputo Fractional Partial Differential EquationsRavi P. Agarwal0Snezhana Hristova1Donal O’Regan2Department of Mathematics, Texas A&M University-Kingsville, Kingsville, TX 78363, USAFaculty of Mathematics and Informatics, Plovdiv University “P. Hilendarski”, 4000 Plovdiv, BulgariaSchool of Mathematical and Statistical Sciences, University of Galway, H91 TK33 Galway, IrelandIn 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.https://www.mdpi.com/2504-3110/7/1/80reaction-diffusion neural networksgeneralized proportional Caputo fractional derivativesdelaysasymptotic behavior |
| spellingShingle | Ravi P. Agarwal Snezhana Hristova Donal O’Regan Asymptotic Behavior of Delayed Reaction-Diffusion Neural Networks Modeled by Generalized Proportional Caputo Fractional Partial Differential Equations Fractal and Fractional reaction-diffusion neural networks generalized proportional Caputo fractional derivatives delays asymptotic behavior |
| title | Asymptotic Behavior of Delayed Reaction-Diffusion Neural Networks Modeled by Generalized Proportional Caputo Fractional Partial Differential Equations |
| title_full | Asymptotic Behavior of Delayed Reaction-Diffusion Neural Networks Modeled by Generalized Proportional Caputo Fractional Partial Differential Equations |
| title_fullStr | Asymptotic Behavior of Delayed Reaction-Diffusion Neural Networks Modeled by Generalized Proportional Caputo Fractional Partial Differential Equations |
| title_full_unstemmed | Asymptotic Behavior of Delayed Reaction-Diffusion Neural Networks Modeled by Generalized Proportional Caputo Fractional Partial Differential Equations |
| title_short | Asymptotic Behavior of Delayed Reaction-Diffusion Neural Networks Modeled by Generalized Proportional Caputo Fractional Partial Differential Equations |
| title_sort | asymptotic behavior of delayed reaction diffusion neural networks modeled by generalized proportional caputo fractional partial differential equations |
| topic | reaction-diffusion neural networks generalized proportional Caputo fractional derivatives delays asymptotic behavior |
| url | https://www.mdpi.com/2504-3110/7/1/80 |
| work_keys_str_mv | AT ravipagarwal asymptoticbehaviorofdelayedreactiondiffusionneuralnetworksmodeledbygeneralizedproportionalcaputofractionalpartialdifferentialequations AT snezhanahristova asymptoticbehaviorofdelayedreactiondiffusionneuralnetworksmodeledbygeneralizedproportionalcaputofractionalpartialdifferentialequations AT donaloregan asymptoticbehaviorofdelayedreactiondiffusionneuralnetworksmodeledbygeneralizedproportionalcaputofractionalpartialdifferentialequations |