Mittag-Leffler stabilization of anti-periodic solutions for fractional-order neural networks with time-varying delays

Dan-Ning Xu; Zhi-Ying Li; Dan-Ning Xu; Zhi-Ying Li

doi:10.3934/math.2023081

AIMS Mathematics

2023, Volume 8, Issue 1: 1610-1619. doi: 10.3934/math.2023081

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Research article

Mittag-Leffler stabilization of anti-periodic solutions for fractional-order neural networks with time-varying delays

Dan-Ning Xu ,
Zhi-Ying Li ^,

The Fundamental Education Department of Yuanpei College, Shaoxing University, Shaoxing 312000, China

Received: 28 July 2022 Revised: 11 September 2022 Accepted: 20 September 2022 Published: 24 October 2022
MSC : 92B20, 34K20

Mittag-Leffler stabilization of anti-periodic solutions for fractional-order neural networks with time-varying delays are investigated in the article. We derive the relationship between the fractional-order integrals of the state function with and without delays through the division of time interval, using the properties of fractional calculus, and initial conditions. Moreover, by constructing the sequence solution of the system function which converges to a continuous function uniformly with the Arzela-Asoli theorem, a sufficient condition is obtained to ensure the existence of an anti-periodic solution and Mittag-Leffler stabilization of the system. In the final, we verify the correctness of the conclusion by numerical simulation.
- fractional-order,
- time-varying delays,
- anti-periodic solutions,
- Mittag-Leffler stabilization,
- neural networks
Citation: Dan-Ning Xu, Zhi-Ying Li. Mittag-Leffler stabilization of anti-periodic solutions for fractional-order neural networks with time-varying delays[J]. AIMS Mathematics, 2023, 8(1): 1610-1619. doi: 10.3934/math.2023081

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Abstract

Mittag-Leffler stabilization of anti-periodic solutions for fractional-order neural networks with time-varying delays are investigated in the article. We derive the relationship between the fractional-order integrals of the state function with and without delays through the division of time interval, using the properties of fractional calculus, and initial conditions. Moreover, by constructing the sequence solution of the system function which converges to a continuous function uniformly with the Arzela-Asoli theorem, a sufficient condition is obtained to ensure the existence of an anti-periodic solution and Mittag-Leffler stabilization of the system. In the final, we verify the correctness of the conclusion by numerical simulation.

References

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