# On Variable-Order Fractional Discrete Neural Networks: Solvability and Stability

Article · Amel Hioual, Adel Ouannas, Taki-Eddine Oussaeif, Giuseppe Grassi, Iqbal M. Batiha, Shaher Momani

- Archive id: doi:10.3390/fractalfract6020119
- Published: 2022-02-18
- Venue: Fractal and Fractional
- DOI: https://doi.org/10.3390/fractalfract6020119
- Citations: 67
- Source URL: https://dx.doi.org/10.3390/fractalfract6020119
- PDF: https://www.mdpi.com/2504-3110/6/2/119/pdf?version=1645435111
- Provenance: openalex

## 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.

_Abstract reproduced under CC-BY (publisher license, via OpenAlex)._

Topics: [AI for Mathematics & Formal Proof](https://space-kitty.com/topics/ai-mathematics)

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