Modelling temporal decay of aftershocks by a solution of the fractional reactive equation

Sánchez, Ewin; Vega-Jorquera, Pedro

doi:10.1016/j.amc.2018.08.022

Cited by 9 publications

(3 citation statements)

References 15 publications

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“…Example. In this subsection, we first introduce a fractional model to describe aftershock frequency in real life, that is, temporal decay feature of aftershocks is characterized by the fractional reactive equation [11,24] C…”

Section: Denote Two Setsmentioning

confidence: 99%

Fractional uncertain differential equations with general memory effects: Existences and alpha-path solutions

Luo

Wu²,

Huang³

2022

NAMC

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General fractional calculus is popular recently. Fractional uncertain differential equations (FUDEs) with general memory effects are proposed in this paper. Firstly, existence and uniqueness theorems of solution for general fractional uncertain differential equations (GFUDEs) is presented, and the analytic solution of a linear one is given. Then the concept of α-path is introduced, and relationship between solution of GFUDE and corresponding α-path is also discussed. In addition, a theorem is proved to obtain the expected value of a monotonic function related to solutions of GFUDEs. Finally, a numerical example is given to better understand the significance of general memory effects. This paper provides more types of FUDEs to better describe some phenomena in uncertain environments.

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Section: Denote Two Setsmentioning

confidence: 99%

Fractional uncertain differential equations with general memory effects: Existences and alpha-path solutions

Luo

Wu²,

Huang³

2022

NAMC

View full text Add to dashboard Cite

show abstract

“…[1,2,3,4,5]). Some recent papers have been devoted to the applications of fractional differential equations in modelling the temporal decay of aftershocks, we refer for example to [6,7]. De facto, fractional derivatives seem to universally appear in mathematical models of epidemic processes (e.g., see [8,9,10,11]), thus playing an important role in handling diffusion and memory mechanisms.…”

Section: Introductionmentioning

confidence: 99%

A fractional approach to study the pure-temporal Epidemic Type Aftershock Sequence (ETAS) process for earthquakes modeling

Cristofaro¹,

Garra²,

Scalas³

et al. 2023

Preprint

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In statistical seismology, the Epidemic Type Aftershocks Sequence (ETAS) model is a branching process used world-wide to forecast earthquake intensity rates and reproduce many statistical features observed in seismicity catalogs. In this paper, we describe a fractional differential equation that governs the earthquake intensity rate of the pure temporal ETAS model by using the Caputo fractional derivative and we solve it analytically.We highlight that the tools and special functions of fractional calculus simplify the classical methods employed to obtain the intensity rate and let us describe the change of solution decay for large times. We also apply and discuss the theoretical results to the Japanese catalog in the period 1965-2003.

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“…[2,7,21,26,27]). Some recent papers have been devoted to the applications of fractional differential equations in modelling the temporal decay of aftershocks, we refer for example to [24,41]. De facto, fractional derivatives seem to universally appear in mathematical models of epidemic processes (e.g., see [1,3,4,33]), thus playing an important role in handling diffusion and memory mechanisms.…”

Section: Introductionmentioning

confidence: 99%

A fractional approach to study the pure-temporal Epidemic Type Aftershock Sequence (ETAS) process for earthquakes modeling

Cristofaro

Garra

Scalas

et al. 2023

Fract Calc Appl Anal

View full text Add to dashboard Cite

In statistical seismology, the Epidemic Type Aftershocks Sequence (ETAS) model is a branching process used world-wide to forecast earthquake intensity rates and reproduce many statistical features observed in seismicity catalogs. In this paper, we describe a fractional differential equation that governs the earthquake intensity rate of the pure temporal ETAS model by using the Caputo fractional derivative and we solve it analytically. We highlight that the tools and special functions of fractional calculus simplify the classical methods employed to obtain the intensity rate and let us describe the change of solution decay for large times. We also apply and discuss the theoretical results to the Japanese catalog in the period 1965-2003.

show abstract

Modelling temporal decay of aftershocks by a solution of the fractional reactive equation

Cited by 9 publications

References 15 publications

Fractional uncertain differential equations with general memory effects: Existences and alpha-path solutions

Fractional uncertain differential equations with general memory effects: Existences and alpha-path solutions

A fractional approach to study the pure-temporal Epidemic Type Aftershock Sequence (ETAS) process for earthquakes modeling

A fractional approach to study the pure-temporal Epidemic Type Aftershock Sequence (ETAS) process for earthquakes modeling

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