https://doi.org/10.1140/epjs/s11734-024-01442-6
Regular Article
Asymptotic stability of fractional linear discrete-time equations with arbitrary time delays
1
School of Mathematics and Statistics, Guizhou University, Guizhou, 550025, Guiyang, People’s Republic of China
2
Key Laboratory of Intelligent Analysis and Decision on Complex Systems, Chongqing University of Posts and Telecommunications, 400065, Chongqing, People’s Republic of China
3
School of Mathematical Sciences, Sichuan Normal University, 610066, Chengdu, People’s Republic of China
Received:
23
July
2024
Accepted:
5
December
2024
Published online:
7
January
2025
This paper introduces a class of Caputo fractional difference equations with arbitrary time delays. It provides non-negative conditions of the Mittag-Leffler function solutions. Exact solutions of fractional linear difference equations are obtained by Picard’s method, and stability conditions are given by the Z-transform. Finally, such results are extended to h-fractional difference equations. This study reveals the time delay’s effect on the dynamics of fractional difference equations and the stable regions. It also provides necessary and sufficient conditions for neural networks and control.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2024
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
