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

Author:

Almatroud Othman Abdullah1,Hioual Amel2ORCID,Ouannas Adel3,Sawalha Mohammed Mossa1,Alshammari Saleh1,Alshammari Mohammad1ORCID

Affiliation:

1. Department of Mathematics, Faculty of Science, University of Ha’il, Ha’il 81451, Saudi Arabia

2. Laboratory of Dynamical Systems and Control, University of Larbi Ben M’hidi, Oum El Bouaghi 04000, Algeria

3. Department of Mathematics and Computer Science, University of Larbi Ben M’hidi, Oum El Bouaghi 04000, Algeria

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.

Funder

Scientific Research Deanship at University of Ha’il-Saudi Arabia

Publisher

MDPI AG

Subject

Statistics and Probability,Statistical and Nonlinear Physics,Analysis

Reference38 articles.

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4. On fractional derivatives with exponential kernel and their discrete versions;Abdeljawad;Rep. Math. Phys.,2017

5. Atangana, A., and Baleanu, D. (2016). New fractional derivatives with nonlocal and non-singular kernel: Theory and application to heat transfer model. arXiv.

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