On Variable-Order Fractional Discrete Neural Networks: Solvability and Stability
Amel Hioual, Adel Ouannas, Taki-Eddine Oussaeif, Giuseppe Grassi, Iqbal M. Batiha, Shaher Momani
Abstract
Few papers have been published to date regarding the stability of neural networks described by fractional difference operators. This paper makes a contribution to the topic by presenting a variable-order fractional discrete neural network model and by proving its Ulam–Hyers stability. In particular, two novel theorems are illustrated, one regarding the existence of the solution for the proposed variable-order network and the other regarding its Ulam–Hyers stability. Finally, numerical simulations of three-dimensional and two-dimensional variable-order fractional neural networks were carried out to highlight the effectiveness of the conceived theoretical approach.