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Finite-Time Stability in Nonhomogeneous Delay Differential Equations of Fractional Hilfer Type

Author

Listed:
  • Ahmed Salem

    (Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia)

  • Rawia Babusail

    (Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia)

Abstract

In the current contribution, integral representations of the solutions of homogeneous and nonhomogeneous delay differential equation of a fractional Hilfer derivative are established in terms of the delayed Mittag-Leffler-type matrix function of two parameters. By using the method of variation of constants, the solution representations are represented. Finite-time stability of the solutions is examined with provision of appropriate sufficient conditions. Finally, an illustrated numerical example is introduced to apply the theoretical results.

Suggested Citation

  • Ahmed Salem & Rawia Babusail, 2022. "Finite-Time Stability in Nonhomogeneous Delay Differential Equations of Fractional Hilfer Type," Mathematics, MDPI, vol. 10(9), pages 1-14, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1520-:d:807436
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    References listed on IDEAS

    as
    1. Ahmed Salem & Kholoud N. Alharbi & Hashim M. Alshehri, 2022. "Fractional Evolution Equations with Infinite Time Delay in Abstract Phase Space," Mathematics, MDPI, vol. 10(8), pages 1-17, April.
    2. Zada, Akbar & Pervaiz, Bakhtawar & Subramanian, Muthaiah & Popa, Ioan-Lucian, 2022. "Finite time stability for nonsingular impulsive first order delay differential systems," Applied Mathematics and Computation, Elsevier, vol. 421(C).
    3. 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.
    4. Ahmed Salem & Noorah Mshary, 2020. "On the Existence and Uniqueness of Solution to Fractional-Order Langevin Equation," Advances in Mathematical Physics, Hindawi, vol. 2020, pages 1-11, October.
    5. Rezapour, Sh. & Kumar, S. & Iqbal, M.Q. & Hussain, A. & Etemad, S., 2022. "On two abstract Caputo multi-term sequential fractional boundary value problems under the integral conditions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 365-382.
    6. Davis, L.C., 2003. "Modifications of the optimal velocity traffic model to include delay due to driver reaction time," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 319(C), pages 557-567.
    7. Khalid Hilal & Lahcen Ibnelazyz & Karim Guida & Said Melliani, 2020. "Fractional Langevin Equations with Nonseparated Integral Boundary Conditions," Advances in Mathematical Physics, Hindawi, vol. 2020, pages 1-8, August.
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    Cited by:

    1. Ahmed Salem & Hunida Malaikah & Eid Sayed Kamel, 2023. "An Infinite System of Fractional Sturm–Liouville Operator with Measure of Noncompactness Technique in Banach Space," Mathematics, MDPI, vol. 11(6), pages 1-17, March.
    2. Ahmed Salem & Lamya Almaghamsi, 2023. "Solvability of Sequential Fractional Differential Equation at Resonance," Mathematics, MDPI, vol. 11(4), pages 1-18, February.

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