@article{Zhang2023, 
author = {Yuehong Zhang and Zhiying Li and Wangdong Jiang and Wei Liu},
title = {The stability of anti-periodic solutions for fractional-order inertial BAM neural networks with time-delays},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {3},
pages = {6176-6190},
keywords = {fractional-order, Mittag-Leffler stability, inertial BAM neural networks, Ascoli-Arzela theorem, anti-periodic solutions},
url = {https://www.sciopen.com/article/10.3934/math.2023312},
doi = {10.3934/math.2023312},
abstract = {The dynamic signal transmission process can be regarded as an anti-periodic process, and fractional-order inertial neural networks are widely used in signal processing and other fields, so anti-periodicity is also regarded as an important dynamic feature of inertial neural networks. This paper mainly studies the existence and Mittag-Leffler stability of anti-periodic solutions for a class of fractional-order inertial BAM neural networks with time-delays. By introducing variable substitution, the model with two different fractional-order derivatives is transformed into a model with only one fractional-order derivative of the same order. Using the properties of fractional-order calculus, the relationship between the fractional-order integral of the state function with and without time-delays is given. Firstly, the sufficient conditions for the boundedness and the Mittag-Leffler stability of the solutions for the system are derived. Secondly, by constructing the sequence solution of the function for the system and applying Ascoli-Arzela theorem, the sufficient conditions for the existence and Mittag-Leffler stability of the anti-periodic solution are given. Finally, the correctness of the conclusion is verified by a numerical example.}
}