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Modeling Aftershocks By Fractional Calculus: Exact Discretization Versus Approximate Discretization

Author

Listed:
  • HUA KONG

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

  • GUANG YANG

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

  • CHENG LUO

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

Abstract

This paper suggests two fractional differences for aftershock modeling with heavy tails. Discrete fractional calculus is a straightforward tool on isolated time scale. On the other hand, the fractional difference also can be derived by standard finite difference method when the difference formula is convergent. The two methods are both adopted and compared in the results. The unknown parameters are determined by use of the least square method where Ya’an earthquake aftershock data is used. It is reported that the discrete fractional calculus is an exact discretization tool without any loss in the memory effects which leads to better results.

Suggested Citation

  • Hua Kong & Guang Yang & Cheng Luo, 2021. "Modeling Aftershocks By Fractional Calculus: Exact Discretization Versus Approximate Discretization," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(08), pages 1-6, December.
    • Handle: RePEc:wsi:fracta:v:29:y:2021:i:08:n:s0218348x21400387
    DOI: 10.1142/S0218348X21400387
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    Cited by:

    1. 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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