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Explicit solutions and finite-time stability for fractional delay systems

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  • Elshenhab, Ahmed M.
  • Wang, Xing Tao
  • Hosny, Mohamed

Abstract

Finite-time stability and explicit solutions are considered for nonhomogeneous fractional systems with pure delay. First, explicit solutions are obtained by using new delayed Mittag-Leffler-type matrix functions. Second, the finite-time stability results are obtained by utilizing these explicit solutions and the norm estimate of these delayed Mittag-Leffler-type matrix functions. The results improve, extend, and complement the previous works. Finally, an example is provided to illustrate the importance of the results.

Suggested Citation

  • Elshenhab, Ahmed M. & Wang, Xing Tao & Hosny, Mohamed, 2025. "Explicit solutions and finite-time stability for fractional delay systems," Applied Mathematics and Computation, Elsevier, vol. 498(C).
    • Handle: RePEc:eee:apmaco:v:498:y:2025:i:c:s0096300325001158
    DOI: 10.1016/j.amc.2025.129388
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    References listed on IDEAS

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    1. Ahmed M. Elshenhab & Xingtao Wang & Clemente Cesarano & Barakah Almarri & Osama Moaaz, 2022. "Finite-Time Stability Analysis of Fractional Delay Systems," Mathematics, MDPI, vol. 10(11), pages 1-11, May.
    2. 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.
    3. Si, Yuanchao & Wang, JinRong & Fečkan, Michal, 2020. "Controllability of linear and nonlinear systems governed by Stieltjes differential equations," Applied Mathematics and Computation, Elsevier, vol. 376(C).
    4. Elshenhab, Ahmed M. & Wang, Xing Tao, 2021. "Representation of solutions of linear differential systems with pure delay and multiple delays with linear parts given by non-permutable matrices," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    5. Nazim I. Mahmudov & Amal M. Almatarneh, 2020. "Stability of Ulam–Hyers and Existence of Solutions for Impulsive Time-Delay Semi-Linear Systems with Non-Permutable Matrices," Mathematics, MDPI, vol. 8(9), pages 1-17, September.
    6. Ahmed M. Elshenhab & Xingtao Wang & Omar Bazighifan & Jan Awrejcewicz, 2022. "Finite-Time Stability Analysis of Linear Differential Systems with Pure Delay," Mathematics, MDPI, vol. 10(9), pages 1-10, April.
    7. Jiale Sheng & Wei Jiang & Denghao Pang & Sen Wang, 2020. "Controllability of Nonlinear Fractional Dynamical Systems with a Mittag–Leffler Kernel," Mathematics, MDPI, vol. 8(12), pages 1-10, December.
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