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

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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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Acknowledgements

This study is supported via funding from Prince Sattam bin Abdulaziz University, project number (PSAU/2023/R/1445).

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Authors and Affiliations

  1. Department of Mathematics and Statistics College of Science, King Faisal University, 31982, Hafuf, Al Ahsa, Saudi Arabia

    Muath Awadalla

  2. Department of Mathematics, Eastern Mediterranean University, 99628, North Cyprus, Famagusta, Turkey

    Nazim I. Mahmudov

  3. Research Center of Econophysics, Azerbaijan State University of Economics (UNEC), Istiqlaliyyat Str. 6, 1001, Baku, Azerbaijan

    Nazim I. Mahmudov

  4. Department of Mathematics College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, 11942, Al-Kharj, Saudi Arabia

    Jihan Alahmadi

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  1. Muath Awadalla
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  2. Nazim I. Mahmudov
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  3. Jihan Alahmadi
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Correspondence to Jihan Alahmadi.

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Awadalla, M., Mahmudov, N.I. & Alahmadi, J. A novel delayed discrete fractional Mittag-Leffler function: representation and stability of delayed fractional difference system. J. Appl. Math. Comput. 70, 1571–1599 (2024). https://doi.org/10.1007/s12190-024-02012-8

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  • DOI: https://doi.org/10.1007/s12190-024-02012-8

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