# Mittag-Leffler stability analysis of fractional discrete-time neural networks via fixed point technique

Article · Guo–Cheng Wu, Thabet Abdeljawad, Jinliang Liu, Dumitru Bǎleanu, Kai-Teng Wu

- Archive id: doi:10.15388/na.2019.6.5
- Published: 2019-11-07
- Venue: Nonlinear Analysis Modelling and Control
- DOI: https://doi.org/10.15388/na.2019.6.5
- Citations: 88
- Source URL: https://doi.org/10.15388/na.2019.6.5
- Provenance: openalex

## Abstract

A class of semilinear fractional difference equations is introduced in this paper. The fixed point theorem is adopted to find stability conditions for fractional difference equations. The complete solution space is constructed and the contraction mapping is established by use of new equivalent sum equations in form of a discrete Mittag-Leffler function of two parameters. As one of the application, finite-time stability is discussed and compared. Attractivity of fractional difference equations is proved, and Mittag-Leffler stability conditions are provided. Finally, the stability results are applied to fractional discrete-time neural networks with and without delay, which show the fixed point technique’s efficiency and convenience.

_Abstract reproduced under CC-BY (publisher license, via OpenAlex)._

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