Mittag-Leffler stability analysis of fractional discrete-time neural networks via fixed point technique
Articles
Guo-Cheng Wu
Neijiang Normal University
Thabet Abdeljawad
Prince Sultan University
Jinliang Liu
Nanjing University of Finance and Economics
Dumitru Baleanu
Cankaya University
Kai-Teng Wu
Neijiang Normal University
Published 2019-11-07
https://doi.org/10.15388/NA.2019.6.5
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Keywords

ractional difference equations
fractional discrete-time neural networks
Mittag-Leffler stability

How to Cite

Wu G.-C., Abdeljawad T., Liu J., Baleanu D. and Wu K.-T. (2019) “Mittag-Leffler stability analysis of fractional discrete-time neural networks via fixed point technique”, Nonlinear Analysis: Modelling and Control, 24(6), pp. 919–936. doi: 10.15388/NA.2019.6.5.

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.

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