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Vestnik KRAUNC. Fiziko-Matematicheskie Nauki, 2023, Volume 45, Number 4, Pages 24–35
DOI: https://doi.org/10.26117/2079-6641-2023-45-4-24-35
(Mi vkam621)
 

This article is cited in 2 scientific papers (total in 2 papers)

MATHEMATICAL MODELING

Fractional model of geoacoustic emission

R. I. Parovik

Institute for Cosmophysical Research and Radio Propagation FEB RAS
References:
Abstract: In this work, a fractional dynamic system that describes high-frequency geoacoustic emission with heredity was proposed and investigated. The model is a system of two connected linear oscillators with nonconstant coefficients and Gerasimov-Caputo fractional order derivatives. Each oscillator describes a dislocation source of geoacoustic emission. The model is built on the assumption that interaction between sources occurs only through radiation. The presence of heredity indicates a change in the intensity of such interaction. For a fractional dynamic model with Gerasimov-Caputo derivatives, local initial conditions are valid, i.e. the Cauchy problem is posed. Further in the work, based on the Gerasimov-Caputo approximation of fractional derivatives, a nonlocal explicit finite-difference scheme is constructed for the numerical solution of the Cauchy problem. The numerical solution is visualized. Oscillograms and phase trajectories were constructed using a numerical algorithm for various values of the orders of fractional derivatives in the Maple computer algebra environment. Some interpretation of the simulation results is given.
Keywords: mathematical modeling, fractional dynamic system, geoacoustic emissions, oscillogram, phase trajectory, explicit finite-difference, Maple.
Funding agency Grant number
Russian Science Foundation 22-11-00064
The research was carried out within the framework of the Russian Science Foundation grant No. 22-11-00064 on the topic «Modeling of dynamic processes in the geospheres taking into account heredity».
Document Type: Article
UDC: 519.642.2
MSC: Primary 34A08; Secondary 34A34
Language: Russian
Citation: R. I. Parovik, “Fractional model of geoacoustic emission”, Vestnik KRAUNC. Fiz.-Mat. Nauki, 45:4 (2023), 24–35
Citation in format AMSBIB
\Bibitem{Par23}
\by R.~I.~Parovik
\paper Fractional model of geoacoustic emission
\jour Vestnik KRAUNC. Fiz.-Mat. Nauki
\yr 2023
\vol 45
\issue 4
\pages 24--35
\mathnet{http://mi.mathnet.ru/vkam621}
\crossref{https://doi.org/10.26117/2079-6641-2023-45-4-24-35}
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  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Vestnik KRAUNC. Fiziko-Matematicheskie Nauki Vestnik KRAUNC. Fiziko-Matematicheskie Nauki
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