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Finite-Time Stability of a Class of Nonstationary Nonlinear Fractional Order Time Delay Systems: New Gronwall–Bellman Inequality Approach

Author

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  • Mihailo P. Lazarević

    (Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Belgrade, Serbia)

  • Stjepko Pišl

    (Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Belgrade, Serbia)

  • Darko Radojević

    (SC “Pinki-Zemun”, Gradski Park 2, Zemun, 11080 Beograd, Serbia)

Abstract

This paper aims to analyze finite-time stability (FTS) for a class of nonstationary nonlinear two-term fractional-order time-delay systems with α , β ∈ 0 , 2 . Using a new type of generalized Gronwall–Bellman inequality, we derive new FTS stability criteria for these systems in terms of the Mittag–Leffler function. We demonstrate that our theoretical results are less conservative than those presented in the existing literature. Finally, we provide three numerical examples using a modified Adams–Bashforth–Moulton algorithm to illustrate the applicability of the proposed stability conditions.

Suggested Citation

  • Mihailo P. Lazarević & Stjepko Pišl & Darko Radojević, 2025. "Finite-Time Stability of a Class of Nonstationary Nonlinear Fractional Order Time Delay Systems: New Gronwall–Bellman Inequality Approach," Mathematics, MDPI, vol. 13(9), pages 1-17, April.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:9:p:1490-:d:1646998
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    References listed on IDEAS

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    1. Du, Feifei & Lu, Jun-Guo, 2021. "New criterion for finite-time synchronization of fractional order memristor-based neural networks with time delay," Applied Mathematics and Computation, Elsevier, vol. 389(C).
    2. Zitane, Hanaa & Torres, Delfim F.M., 2023. "Finite time stability of tempered fractional systems with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    3. Panda, Sumati Kumari & Vijayakumar, Velusamy, 2023. "Results on finite time stability of various fractional order systems," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    4. Du, Feifei & Lu, Jun-Guo, 2020. "Finite-time stability of neutral fractional order time delay systems with Lipschitz nonlinearities," Applied Mathematics and Computation, Elsevier, vol. 375(C).
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