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Analytical Solution of the Fractional Linear Time‐Delay Systems and their Ulam‐Hyers Stability

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  • Nazim I. Mahmudov

Abstract

We introduce the delayed Mittag‐Leffler type matrix functions, delayed fractional cosine, and delayed fractional sine and use the Laplace transform to obtain an analytical solution to the IVP for a Hilfer type fractional linear time‐delay system D0,tμ,νzt+Azt+Ωzt−h=ft of order 1

Suggested Citation

  • Nazim I. Mahmudov, 2022. "Analytical Solution of the Fractional Linear Time‐Delay Systems and their Ulam‐Hyers Stability," Journal of Applied Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jnljam:v:2022:y:2022:i:1:n:2661343
    DOI: 10.1155/2022/2661343
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    References listed on IDEAS

    as
    1. Nazim I. Mahmudov & Yansheng Liu, 2022. "Analytical Solution of the Fractional Linear Time-Delay Systems and their Ulam-Hyers Stability," Journal of Applied Mathematics, Hindawi, vol. 2022, pages 1-7, September.
    2. Josef Diblík & Blanka Morávková, 2014. "Representation of the Solutions of Linear Discrete Systems with Constant Coefficients and Two Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    3. Hari M. Srivastava & Khaled Mohammed Saad & Walid M. Hamanah, 2022. "Certain New Models of the Multi-Space Fractal-Fractional Kuramoto-Sivashinsky and Korteweg-de Vries Equations," Mathematics, MDPI, vol. 10(7), pages 1-13, March.
    4. Nazim I. Mahmudov & Amal M. Almatarneh, 2020. "Stability of Ulam–Hyers and Existence of Solutions for Impulsive Time-Delay Semi-Linear Systems with Non-Permutable Matrices," Mathematics, MDPI, vol. 8(9), pages 1-17, September.
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