On Variable-Order Fractional Discrete Neural Networks: Existence, Uniqueness and Stability

Abstract

Given the recent advances regarding the studies of discrete fractional calculus, and the fact that the dynamics of discrete-time neural networks in fractional variable-order cases have not been sufficiently documented, herein, we consider a novel class of discrete-time fractional-order neural networks using discrete nabla operator of variable-order. An adequate criterion for the existence of the solution in addition to its uniqueness for such systems is provided with the use of Banach fixed point technique. Moreover, the uniform stability is investigated. We provide at the end two numerical simulations illustrating the relevance of the aforementioned results.

Keywords

• discrete fractional variable-order neural networks
• discrete nabla variable-orde fractional operators
• Banach fixed point theorem
• uniform stability