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

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.

Stability analysis of fractional-order systems with randomly time-varying parameters

“…In order to find out the essential performance of the established equations, the existence and stability of the solutions of the equations is the first prerequisite. In the last few years, several results on this topic were presented including asymptotic stability [1,4,15,24]), exponential stability [2,25] and Mittag-Leffler stability [5,19,[27][28][29][30]. The general method for analyzing the stability is based on the first method of Lyapunov, the second method of Lyapunov and other mathematical techniques.…”

Mittag-Leffler–Hyers–Ulam stability of differential equation using Fourier transform

“…Using the Hyers-Ulam method, Wu and Baleanu [8] proved the Mittag-Leffler stability of impulsive fractional difference equations; Wu, Baleanu, and Huang [9] proved the Mittag-Leffler stability of linear fractional delay difference equations with impulse, and Wu et al [10] investigated the Mittag-Leffler stability analysis of fractional discrete-time neural networks via the fixed point technique.…”

Stability analysis of a nonlinear coupled implicit switched singular fractional differential system with p-Laplacian

“…Different fixed point theorems, which have numerous applications in the mentioned equations, are presented. Few important fixed point theorems can be found in [18,39,46].…”