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RESEARCH ARTICLE

Analysis and analytical solution of incommensurate fuzzy fractional nabla difference systems in neural networks

Babak Shiri1* ,  Ehsan Dadkhah Khiabani2 ,  Dumitru Baleanu3,4
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1 Key Laboratory of Numerical Simulation for Sichuan Provincial Universities, College of Mathematics and Information Science, Neijiang Normal University, Neijang, China
2 Faculty of Civil Engineering, University of Tabriz, Tabriz, Iran
3 Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
4 Institute of Space Sciences-subsidiary of INFLPR, Magurele-Bucharest, Romania
IJOCTA, 025130067 https://doi.org/10.36922/IJOCTA025130067
Received: 30 March 2025 | Revised: 12 June 2025 | Accepted: 25 June 2025 | Published online: 18 July 2025
© 2025 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
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Abstract

Uncertain incommensurate fractional nabla difference systems (IFDSs) in recurrent neural networks (RNNs) are analyzed using fuzzy number theory to address input uncertainties. Fuzzy number theory and its operations are reinvestigated, and the H-differenceable concept is introduced. The existence of a unique H-differenceable solution for incommensurate RNNs is proved. A recursive algorithm is proposed to obtain fuzzy solutions. Illustrative examples with 2-dimensional IFDSs are provided to validate the framework for integrating fractional calculus, fuzzy dynamics and incommensurate RNNs.

Keywords
Fuzzy numbers
Fuzzy neural networks
Incommensurate systems
Nabla fractional difference
Recurrent neural networks
Uncertainty analysis
Funding
This research is supported by the Neijiang Normal University school-level science and technology project (key project, No. XJ2024008301) and Sharestan retrofit design co.
Conflict of interest
The authors declare that they have no conflict of interest to disclose.
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An International Journal of Optimization and Control: Theories & Applications, Electronic ISSN: 2146-5703 Print ISSN: 2146-0957, Published by AccScience Publishing
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