Finite-Time Stability of ABC Type ℏ-Fractional Discrete Neural Networks: Gronwall Inequality and Stability Criterion
Amel Hioual, Adel Ouannas, Shaher Momani, Taki-Eddine Oussaeif
Abstract
The dynamics of fractional-order difference neural networks are currently a major research area, with several noteworthy discoveries. The dynamics of discrete-time neural networks with $\hbar$-fractional nonlocal and nonsingular kernels, on the other hand, have not been thoroughly researched, and this paper is one of the first to address this subject. The main focus of this research is the finite-time stability of discrete-time neural networks based on the nabla ABC fractional difference operator. First, the Atangana-Baleanu $\hbar$-fractional difference sum operator is used to investigate a generalized $\hbar$-Gronwall inequality. This inequality also yields the uniqueness theorem and the finite-time stability criterion of nonlinear $\hbar$-fractional neural networks. Finally, several examples are offered to show the effectiveness of our theoretical conclusion.