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Mittag-Leffler Stability Analysis Of Tempered Fractional Neural Networks With Short Memory And Variable-Order

Author

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  • CHUAN-YUN GU

    (School of Mathematics, Sichuan University of Arts and Science, Dazhou 635000, P. R. China)

  • FENG-XIA ZHENG

    (School of Mathematics, Sichuan University of Arts and Science, Dazhou 635000, P. R. China2Department of Mathematics, Sichuan University, Chengdu 610064, P. R. China)

  • BABAK SHIRI

    (Data Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, P. R. China)

Abstract

A class of tempered fractional neural networks is proposed in this paper. Stability conditions for tempered fractional neural networks are provided by using Banach fixed point theorem. Attractivity and Mittag-Leffler stability are given. In order to show the efficiency and convenience of the method used, tempered fractional neural networks with and without delay are discussed, respectively. Furthermore, short memory and variable-order tempered fractional neural networks are proposed under the global conditions. Finally, two numerical examples are used to demonstrate the theoretical results.

Suggested Citation

  • Chuan-Yun Gu & Feng-Xia Zheng & Babak Shiri, 2021. "Mittag-Leffler Stability Analysis Of Tempered Fractional Neural Networks With Short Memory And Variable-Order," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(08), pages 1-12, December.
    • Handle: RePEc:wsi:fracta:v:29:y:2021:i:08:n:s0218348x21400296
    DOI: 10.1142/S0218348X21400296
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    Cited by:

    1. Zitane, Hanaa & Torres, Delfim F.M., 2023. "Finite time stability of tempered fractional systems with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    2. Ravi P. Agarwal & Snezhana Hristova & Donal O’Regan, 2023. "Inequalities for Riemann–Liouville-Type Fractional Derivatives of Convex Lyapunov Functions and Applications to Stability Theory," Mathematics, MDPI, vol. 11(18), pages 1-23, September.

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