MODELING AFTERSHOCKS BY FRACTIONAL CALCULUS: EXACT DISCRETIZATION VERSUS APPROXIMATE DISCRETIZATION

Hua Kong (), Guang Yang and Cheng Luo ()
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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

FRACTALS (fractals), 2021, vol. 29, issue 08, 1-6

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.

Keywords: Decay Rate of Aftershocks; Fractional Calculus; Time Scale (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21400387

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