A novel delayed discrete fractional Mittag-Leffler function: representation and stability of delayed fractional difference system

Muath Awadalla; Nazim I. Mahmudov; Jihan Alahmadi

doi:10.1007/s12190-024-02012-8

A novel delayed discrete fractional Mittag-Leffler function: representation and stability of delayed fractional difference system

Muath Awadalla, Nazim I. Mahmudov, Jihan Alahmadi

Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

In this paper, a delayed discrete Mittag-Leffler matrix function generated by two noncommutative square matrices is introduced. Utilizing this function, the paper establishes an explicit expression for solving constant delay fractional difference systems. Additionally, a criterion for determining the Ulam-Hyers stability of delay fractional difference systems with constant coefficients is derived using the aforementioned explicit representation formula.

Original language	English
Pages (from-to)	1571-1599
Number of pages	29
Journal	Journal of Applied Mathematics and Computing
Volume	70
Issue number	2
DOIs	https://doi.org/10.1007/s12190-024-02012-8
State	Published - Apr 2024

Keywords

33E12
39A30
Discrete delayed perturbation
Fractional difference system
Nabla discrete Mittag-Leffler function
Time-delay

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10.1007/s12190-024-02012-8

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abstract = "In this paper, a delayed discrete Mittag-Leffler matrix function generated by two noncommutative square matrices is introduced. Utilizing this function, the paper establishes an explicit expression for solving constant delay fractional difference systems. Additionally, a criterion for determining the Ulam-Hyers stability of delay fractional difference systems with constant coefficients is derived using the aforementioned explicit representation formula.",

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AU - Mahmudov, Nazim I.

AU - Alahmadi, Jihan

N1 - Publisher Copyright: © The Author(s) under exclusive licence to Korean Society for Informatics and Computational Applied Mathematics 2024.

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N2 - In this paper, a delayed discrete Mittag-Leffler matrix function generated by two noncommutative square matrices is introduced. Utilizing this function, the paper establishes an explicit expression for solving constant delay fractional difference systems. Additionally, a criterion for determining the Ulam-Hyers stability of delay fractional difference systems with constant coefficients is derived using the aforementioned explicit representation formula.

AB - In this paper, a delayed discrete Mittag-Leffler matrix function generated by two noncommutative square matrices is introduced. Utilizing this function, the paper establishes an explicit expression for solving constant delay fractional difference systems. Additionally, a criterion for determining the Ulam-Hyers stability of delay fractional difference systems with constant coefficients is derived using the aforementioned explicit representation formula.

KW - 33E12

KW - 39A30

KW - Discrete delayed perturbation

KW - Fractional difference system

KW - Nabla discrete Mittag-Leffler function

KW - Time-delay

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A novel delayed discrete fractional Mittag-Leffler function: representation and stability of delayed fractional difference system

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Keywords

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