MODELING AFTERSHOCKS BY FRACTIONAL CALCULUS: EXACT DISCRETIZATION VERSUS APPROXIMATE DISCRETIZATION

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.

Automated summary

This paper suggests two fractional differences for aftershock modeling with heavy tails, using discrete fractional calculus and standard finite difference method. The results show that discrete fractional calculus is an exact discretization tool without any loss in memory effects, leading to better modeling results.