Stability and Solvability of Discrete Generalized Proportional Caputo Fractional Neural Network Models

Martin Bohner; Rajrani Gupta

doi:10.5644/SJM.21.02.02

Authors

Martin Bohner Missouri University of Science and Technology, Department of Mathematics, Rolla, MO, USA https://orcid.org/0000-0001-8310-0266
Rajrani Gupta Missouri University of Science and Technology, Department of Mathematics, Rolla, MO, USA https://orcid.org/0009-0008-5847-3915

DOI:

https://doi.org/10.5644/SJM.21.02.02

Keywords:

Generalized Caputo proportional fractional difference, variable-order fractional neural networks, Krasnoselskii's fixed-point theorem, Ulam-Hyers stability

Abstract

This study examines the stability in variable-order fractional discrete neural networks modeled via the generalized proportional Caputo fractional difference operator. By employing the Krasnoselskii fixed-point theorem, we establish solution existence under Lipschitz continuity, and we prove Ulam–Hyers stability. Numerical simulations validate that balancing network parameters and fractional orders ensure robustness.

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