Nonlinear nabla variable-order fractional discrete systems: Asymptotic stability and application to neural networks

Variable-order fractional discrete models are dynamical systems described by non -integer order difference equations where the fractional order changes over discrete-time. This paper makes a contribution to the topic by presenting two nonlinear nabla variable-order models and by rigorously proving their asymptotic stability. In particular, some novel theorems are illustrated, regarding the asymptotic stability of both nonlinear nabla variable-order systems and nonlinear nabla variable-order neural networks. Finally, nu-merical simulations of discrete systems where the fractional order varies with nonlinear law are carried out, with the aim to show the effectiveness of the conceived theoretical approach. (c) 2022 Elsevier B.V. All rights reserved.