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

Nazim Mahmudov and Areen Al-Khateeb
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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

Mathematics, 2020, vol. 8, issue 8, 1-17

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.

Keywords: mittag-leffler type matrix function; Hadamard type derivative; Ulam–Hyers stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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