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Synchronization of Fractional-Order Neural Networks with Time Delays and Reaction-Diffusion Terms via Pinning Control

Author

Listed:
  • M. Hymavathi

    (Department of Mathematics, Thiruvalluvar University, Vellore 632115, Tamil Nadu, India
    These authors contributed equally to this work.)

  • Tarek F. Ibrahim

    (Department of Mathematics, Faculty of Sciences and Arts (Mahayel), King Khalid University, Abha, Saudi Arabia
    Department of Mathematics, Faculty of Sciences, Mansoura University, Mansoura 35516, Egypt
    These authors contributed equally to this work.)

  • M. Syed Ali

    (Department of Mathematics, Thiruvalluvar University, Vellore 632115, Tamil Nadu, India
    These authors contributed equally to this work.)

  • Gani Stamov

    (Department of Mathematics, University of Texas at San Antonio, San Antonio, TX 78249, USA
    These authors contributed equally to this work.)

  • Ivanka Stamova

    (Department of Mathematics, University of Texas at San Antonio, San Antonio, TX 78249, USA
    These authors contributed equally to this work.)

  • B. A. Younis

    (Department of Mathematics, Faculty of Sciences and Arts in Zahran Alganoob, King Khalid University, Abha, Saudi Arabia
    These authors contributed equally to this work.)

  • Khalid I. Osman

    (Department of Mathematics, Faculty of Sciences and Arts in Sarat Abeda, King Khalid University, Abha, Saudi Arabia
    These authors contributed equally to this work.)

Abstract

This paper introduces a novel synchronization scheme for fractional-order neural networks with time delays and reaction-diffusion terms via pinning control. We consider Caputo fractional derivatives, constant delays and distributed delays in our model. Based on the stability behavior, fractional inequalities and Lyapunov-type functions, several criteria are derived, which ensure the achievement of a synchronization for the drive-response systems. The obtained criteria are easy to test and are in the format of inequalities between the system parameters. Finally, numerical examples are presented to illustrate the results. The obtained criteria in this paper consider the effect of time delays as well as the reaction-diffusion terms, which generalize and improve some existing results.

Suggested Citation

  • M. Hymavathi & Tarek F. Ibrahim & M. Syed Ali & Gani Stamov & Ivanka Stamova & B. A. Younis & Khalid I. Osman, 2022. "Synchronization of Fractional-Order Neural Networks with Time Delays and Reaction-Diffusion Terms via Pinning Control," Mathematics, MDPI, vol. 10(20), pages 1-18, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3916-:d:949823
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    References listed on IDEAS

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