Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.17390 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929690481000448 |
|---|---|
| author | Van Thinh, La Tuan, Hoang The Wang, Dongling Yang, Yin |
| author_facet | Van Thinh, La Tuan, Hoang The Wang, Dongling Yang, Yin |
| contents | This paper introduces a generalized fractional Halanay-type coupled inequality, which serves as a robust tool for characterizing the asymptotic stability of diverse time fractional functional differential equations, particularly those exhibiting Mittag-Leffler type stability. Our main tool is a sub-additive property of Mittag-Leffler function and its optimal asymptotic decay rate estimation. Our results further optimize and improve some existing results in the literature. We illustrate two significant applications of this fractional Halanay-type inequality. Firstly, by combining our results in this work with the positive representation method positive representation of delay differential systems, we establish an asymptotic stability criterion for a category of linear fractional coupled systems with bounded delays. This criterion extends beyond the traditional boundaries of positive system theory, offering a new perspective on stability analysis in this domain. Secondly, through energy estimation, we establish the contractility and dissipativity of a class of time fractional neutral functional differential equations. Our analysis reveals the typical long-term polynomial decay behavior inherent in time fractional evolutionary equations, thereby providing a solid theoretical foundation for subsequent numerical investigations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_17390 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fractional coupled Halanay inequality and its applications Van Thinh, La Tuan, Hoang The Wang, Dongling Yang, Yin Numerical Analysis This paper introduces a generalized fractional Halanay-type coupled inequality, which serves as a robust tool for characterizing the asymptotic stability of diverse time fractional functional differential equations, particularly those exhibiting Mittag-Leffler type stability. Our main tool is a sub-additive property of Mittag-Leffler function and its optimal asymptotic decay rate estimation. Our results further optimize and improve some existing results in the literature. We illustrate two significant applications of this fractional Halanay-type inequality. Firstly, by combining our results in this work with the positive representation method positive representation of delay differential systems, we establish an asymptotic stability criterion for a category of linear fractional coupled systems with bounded delays. This criterion extends beyond the traditional boundaries of positive system theory, offering a new perspective on stability analysis in this domain. Secondly, through energy estimation, we establish the contractility and dissipativity of a class of time fractional neutral functional differential equations. Our analysis reveals the typical long-term polynomial decay behavior inherent in time fractional evolutionary equations, thereby providing a solid theoretical foundation for subsequent numerical investigations. |
| title | Fractional coupled Halanay inequality and its applications |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2501.17390 |