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Asymptotic Stability of the Solutions of Neutral Linear Fractional System with Nonlinear Perturbation

Author

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  • Andrey Zahariev

    (Faculty of Mathematics and Informatics, University of Plovdiv, 4000 Plovdiv, Bulgaria)

  • Hristo Kiskinov

    (Faculty of Mathematics and Informatics, University of Plovdiv, 4000 Plovdiv, Bulgaria)

Abstract

In this article existence and uniqueness of the solutions of the initial problem for neutral nonlinear differential system with incommensurate order fractional derivatives in Caputo sense and with piecewise continuous initial function is proved. A formula for integral presentation of the general solution of a linear autonomous neutral system with several delays is established and used for the study of the stability properties of a neutral autonomous nonlinear perturbed linear fractional differential system. Natural sufficient conditions are found to ensure that from global asymptotic stability of the zero solution of the linear part of a nonlinearly perturbed system it follows global asymptotic stability of the zero solution of the whole nonlinearly perturbed system.

Suggested Citation

  • Andrey Zahariev & Hristo Kiskinov, 2020. "Asymptotic Stability of the Solutions of Neutral Linear Fractional System with Nonlinear Perturbation," Mathematics, MDPI, vol. 8(3), pages 1-18, March.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:3:p:390-:d:330930
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    References listed on IDEAS

    as
    1. Li, Mengmeng & Wang, JinRong, 2018. "Exploring delayed Mittag-Leffler type matrix functions to study finite time stability of fractional delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 324(C), pages 254-265.
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    Cited by:

    1. Hristo Kiskinov & Mariyan Milev & Andrey Zahariev, 2022. "About the Resolvent Kernel of Neutral Linear Fractional System with Distributed Delays," Mathematics, MDPI, vol. 10(23), pages 1-17, December.
    2. Hristo Kiskinov & Ekaterina Madamlieva & Magdalena Veselinova & Andrey Zahariev, 2021. "Existence of Absolutely Continuous Fundamental Matrix of Linear Fractional System with Distributed Delays," Mathematics, MDPI, vol. 9(2), pages 1-18, January.
    3. Ekaterina Madamlieva & Hristo Kiskinov & Milena Petkova & Andrey Zahariev, 2022. "On the Preservation with Respect to Nonlinear Perturbations of the Stability Property for Nonautonomous Linear Neutral Fractional Systems with Distributed Delays," Mathematics, MDPI, vol. 10(15), pages 1-20, July.

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