Fractional Neural Networks: Finite time stability and its application to synchronization

Fractiona1-order discrete-time neural networks are kind of discrete-time models described by fractional-order difference operators. Despite the fact that the stability of such networks is required for their effective implementations, extremely low publications on the subject have been published. In this article, finite-time stability of fractional difference neural networks with discrete Mittag-Leffler kernels is investigated. First, with the use a new generalization of the Gronwall inequality by means of the Atangana-Baleanu fractional difference sum operator, we generate some finite-time stability conditions of the discrete-time neural networks in their fractional-order cases with discrete Mittag-Leffler kernel. Then, the finite time stability coupled with the modified Gronwall inequality requirements are used to establish an adequate condition, which can provide these networks with a finite-time synchronization on the basis of a specific state feedback control approach. In addition, we develop a type of variable fractional-order discrete-time neural networks as well as we establish a new theorem that can be used to guarantee the finite-time stability of these networks. Finally, with the use of some performed numerical solutions, the discrete-time fractional-order neural networks are investigated to validate the gained findings.