Mittag-Leffler projective synchronization of uncertain fractional-order fuzzy complex valued neural networks with distributed and time-varying delays

Yang Xu; Zhouping Yin; Yuanzhi Wang; Qi Liu; Anwarud Din; Yang Xu; Zhouping Yin; Yuanzhi Wang; Qi Liu; Anwarud Din

doi:10.3934/math.20241249

AIMS Mathematics

2024, Volume 9, Issue 9: 25577-25602. doi: 10.3934/math.20241249

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Research article

Mittag-Leffler projective synchronization of uncertain fractional-order fuzzy complex valued neural networks with distributed and time-varying delays

1.
School of Mathematics and Physics, Anqing Normal University, Anqing 246133, China
2.
School of Computer and Information Technology, Anqing Normal University, Anqing 246133, China
3.
Department of Mathematics, Sun Yat-sen University, Guangzhou 510275, China

Received: 02 May 2024 Revised: 18 June 2024 Accepted: 23 July 2024 Published: 02 September 2024
MSC : 93D05, 93D15

To study the Mittag-Leffler projective synchronization (MLPS) problem of fractional-order fuzzy neural networks (FOFNNs), in this work we introduced the FOFNNs model. On this basis, we discussed the MLPS of uncertain fractional-order fuzzy complex valued neural networks (FOFCVNNs) with distributed and time-varying delays. Utilizing Banach contraction mapping principle, we proved the existence and uniqueness of the model solution. Moreover, employing the construction of a new hybrid controller, an adaptive hybrid controller, and the fractional-order Razumikhin theorem, algebraic criteria was obtained for implementing MLPS. The algebraic inequality criterion obtained in this article improves and extends the previously published results on MLPS, making it easy to prove and greatly reducing the computational complexity. Finally, different Caputo derivatives of different orders were given, and four numerical examples were provided to fully verify the accuracy of the modified criterion.
- fuzzy neural networks,
- Mittag-Leffler projective synchronization,
- hybrid controller,
- parameter uncertainty,
- time delays
Citation: Yang Xu, Zhouping Yin, Yuanzhi Wang, Qi Liu, Anwarud Din. Mittag-Leffler projective synchronization of uncertain fractional-order fuzzy complex valued neural networks with distributed and time-varying delays[J]. AIMS Mathematics, 2024, 9(9): 25577-25602. doi: 10.3934/math.20241249

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Abstract

To study the Mittag-Leffler projective synchronization (MLPS) problem of fractional-order fuzzy neural networks (FOFNNs), in this work we introduced the FOFNNs model. On this basis, we discussed the MLPS of uncertain fractional-order fuzzy complex valued neural networks (FOFCVNNs) with distributed and time-varying delays. Utilizing Banach contraction mapping principle, we proved the existence and uniqueness of the model solution. Moreover, employing the construction of a new hybrid controller, an adaptive hybrid controller, and the fractional-order Razumikhin theorem, algebraic criteria was obtained for implementing MLPS. The algebraic inequality criterion obtained in this article improves and extends the previously published results on MLPS, making it easy to prove and greatly reducing the computational complexity. Finally, different Caputo derivatives of different orders were given, and four numerical examples were provided to fully verify the accuracy of the modified criterion.

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