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Finite time stability of fractional delay difference systems: A discrete delayed Mittag-Leffler matrix function approach

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  • Du, Feifei
  • Jia, Baoguo

Abstract

A discrete delayed Mittag-Leffler matrix function is developed in this paper. Based on this function, an explicit formula of the solution of fractional delay difference system (FDDS) is derived. Furthermore, a criterion on finite time stability (FTS) of FDDS with constant coefficients is obtained by use of this formula. However, it can’t be directly used to investigate the FTS of FDDS with variable coefficients. To overcome this difficulty, a comparison theorem of FDDS is established to obtain a criterion of the FTS of FDDS with variable coefficients. Finally, a numerical example is given to show the effectiveness of the proposed results.

Suggested Citation

  • Du, Feifei & Jia, Baoguo, 2020. "Finite time stability of fractional delay difference systems: A discrete delayed Mittag-Leffler matrix function approach," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    • Handle: RePEc:eee:chsofr:v:141:y:2020:i:c:s0960077920308237
    DOI: 10.1016/j.chaos.2020.110430
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    References listed on IDEAS

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    1. Abdeljawad, Thabet, 2019. "Fractional difference operators with discrete generalized Mittag–Leffler kernels," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 315-324.
    2. Li, Mengmeng & Wang, JinRong, 2018. "Exploring delayed Mittag-Leffler type matrix functions to study finite time stability of fractional delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 324(C), pages 254-265.
    3. Jan Čermák & Tomáš Kisela & Luděk Nechvátal, 2011. "Discrete Mittag-Leffler Functions in Linear Fractional Difference Equations," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-21, June.
    4. Wu, Guo-Cheng & Baleanu, Dumitru & Luo, Wei-Hua, 2017. "Lyapunov functions for Riemann–Liouville-like fractional difference equations," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 228-236.
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    Cited by:

    1. Chen, Yuting & Li, Xiaoyan & Liu, Song, 2021. "Finite-time stability of ABC type fractional delay difference equations," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    2. Du, Feifei & Lu, Jun-Guo, 2021. "Explicit solutions and asymptotic behaviors of Caputo discrete fractional-order equations with variable coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    3. Ivan Pavlenko & Marek Ochowiak & Praveen Agarwal & Radosław Olszewski & Bernard Michałek & Andżelika Krupińska, 2021. "Improvement of Mathematical Model for Sedimentation Process," Energies, MDPI, vol. 14(15), pages 1-12, July.

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