Abstract
The (integer order) Halanay inequality with distributed delays is extended to the fractional order case. It is proved that solutions decay to zero as a Mittag-Leffler function as time goes to infinity provided that the delay feedback are bounded by similar functions. An application to a problem arising in neural network theory is provided showing that the equilibrium is Mittag-Leffler stable.
| Original language | English |
|---|---|
| Pages (from-to) | 1605-1618 |
| Number of pages | 14 |
| Journal | Acta Mathematica Scientia |
| Volume | 39 |
| Issue number | 6 |
| DOIs | |
| State | Published - 1 Nov 2019 |
Bibliographical note
Publisher Copyright:© 2019, Wuhan Institute Physics and Mathematics, Chinese Academy of Sciences.
Keywords
- 26A33
- 34K37
- 92B20
- Caputo fractional derivative
- Hopfield neural network
- Mittag-Leffler stability
- fractional Halanay inequality
ASJC Scopus subject areas
- General Mathematics
- General Physics and Astronomy
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