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Mittag-Leffler stability and synchronization for FOQVFNNs including proportional delay and Caputo derivative via fractional differential inequality approach

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Abstract

This article discusses the dynamics of Caputo fractional-order quaternion-valued fuzzy neural networks (FOQVFNNs) including proportional delay and derivative order interval \((0,1)\cup (1,2)\). By constructing a fractional-order differential equation according to the fractional differential inequality, a novel lemma is proposed in terms of the Laplace transform approach. Combining the Mittag-Leffler function, Lyapunov direct method, fuzzy inequality technique and the new lemma, several ML stability and synchronization results for FOQVFNNs under the different controller designs are established. The obtained criteria are concise and applicable in the form of algebraic inequalities. Three numerical simulation examples are given to further illustrate the theoretical results.

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Acknowledgements

We would like to express our sincere thanks to Editors and anonymous Reviewers for their valuable suggestions and constructive comments to improve this paper. This work was supported by the Natural Science Foundation of Anhui Province of China (No. 1908085MA01).

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Authors and Affiliations

  1. School of Mathematics and Physics, Anqing Normal University, Anqing, 246133, People’s Republic of China

    Hai Zhang, Chen Wang, Weiwei Zhang & Hongmei Zhang

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  1. Hai Zhang
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  2. Chen Wang
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  3. Weiwei Zhang
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  4. Hongmei Zhang
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Correspondence to Hai Zhang.

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Communicated by Roberto Garrappa.

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Zhang, H., Wang, C., Zhang, W. et al. Mittag-Leffler stability and synchronization for FOQVFNNs including proportional delay and Caputo derivative via fractional differential inequality approach. Comp. Appl. Math. 41, 344 (2022). https://doi.org/10.1007/s40314-022-02062-3

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  • DOI: https://doi.org/10.1007/s40314-022-02062-3

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