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Tempered Fractional Calculus On Time Scale For Discrete-Time Systems

Author

Listed:
  • HUI FU

    (Data Recover Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, P. R. China)

  • LAN-LAN HUANG

    (Data Recover Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, P. R. China)

  • THABET ABDELJAWAD

    (Department of Mathematics and General Sciences, Prince Sultan University, P.O. Box 66833, 11586 Riyadh, Saudi Arabia)

  • CHENG LUO

    (School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210023, P. R. China)

Abstract

The fractional derivative holds historical dependence or non-locality and it becomes a powerful tool in many real-world applications. But it also brings error accumulation of the numerical solutions as well as the theoretical analysis since many properties from the integer order case cannot hold. This paper defines the tempered fractional derivative on an isolated time scale and suggests a new method based on the time scale theory for numerical discretization. Some useful properties like composition law and equivalent fractional sum equations are derived for theoretical analysis. Finally, numerical formulas of fractional discrete systems are provided. As a special case for the step size h = 1, a fractional logistic map with two-parameter memory effects is reported.

Suggested Citation

  • Hui Fu & Lan-Lan Huang & Thabet Abdeljawad & Cheng Luo, 2021. "Tempered Fractional Calculus On Time Scale For Discrete-Time Systems," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(08), pages 1-9, December.
    • Handle: RePEc:wsi:fracta:v:29:y:2021:i:08:n:s0218348x21400338
    DOI: 10.1142/S0218348X21400338
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    Citations

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    Cited by:

    1. Kamsing Nonlaopon & Pshtiwan Othman Mohammed & Y. S. Hamed & Rebwar Salih Muhammad & Aram Bahroz Brzo & Hassen Aydi, 2022. "Analytical and Numerical Monotonicity Analyses for Discrete Delta Fractional Operators," Mathematics, MDPI, vol. 10(10), pages 1-9, May.
    2. Yao, Yu & Wu, Li-Bing, 2022. "Backstepping control for fractional discrete-time systems," Applied Mathematics and Computation, Elsevier, vol. 434(C).

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