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Existence and Stability Results on Hadamard Type Fractional Time-Delay Semilinear Differential Equations

Author

Listed:
  • Nazim Mahmudov

    (Department of Mathematics, Eastern Mediterranean University, Famagusta 99628, T.R. North Cyprus, Mersin 10, Turkey)

  • Areen Al-Khateeb

    (Department of Support Courses, Jadara University, P.O.Box 733, Irbid 21110, Jordan)

Abstract

A delayed perturbation of the Mittag-Leffler type matrix function with logarithm is proposed. This combines the classic Mittag–Leffler type matrix function with a logarithm and delayed Mittag–Leffler type matrix function. With the help of this introduced delayed perturbation of the Mittag–Leffler type matrix function with a logarithm, we provide an explicit form for solutions to non-homogeneous Hadamard-type fractional time-delay linear differential equations. We also examine the existence, uniqueness, and Ulam–Hyers stability of Hadamard-type fractional time-delay nonlinear equations.

Suggested Citation

  • Nazim Mahmudov & Areen Al-Khateeb, 2020. "Existence and Stability Results on Hadamard Type Fractional Time-Delay Semilinear Differential Equations," Mathematics, MDPI, vol. 8(8), pages 1-17, July.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:8:p:1242-:d:391969
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    References listed on IDEAS

    as
    1. Mohammed M. Matar, 2018. "Solution of Sequential Hadamard Fractional Differential Equations by Variation of Parameter Technique," Abstract and Applied Analysis, Hindawi, vol. 2018, pages 1-7, February.
    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.
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