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

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

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 ty...

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Bibliographic Details
Main Authors: Nazim Mahmudov, Areen Al-Khateeb
Format: Article
Language:English
Published: MDPI AG 2020-07-01
Series:Mathematics
Subjects:
mittag-leffler type matrix function
Hadamard type derivative
Ulam–Hyers stability
Online Access:https://www.mdpi.com/2227-7390/8/8/1242
Description
Summary: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.
ISSN:2227-7390

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