Vestnik КRAUNC. Fiz.-Mat. nauki. 2023. vol. 45. no. 4. P. 24-35. ISSN 2079-6641

Research Article
Full text in Russian
MSC 34A08, 34A34

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Fractional Model of Geoacoustic Emission

R. I. Parovik^\ast

Institute for Cosmophysical Research and Radio Propagation FEB RAS, 684034, v. Paratunka,
Mirnaya st., 7, Russia

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.

Key words: mathematical modeling, fractional dynamic system, geoacoustic emissions, oscillogram, phase
trajectory, explicit finite-difference, Maple

Received: 07.11.2023; Revised: 18.11.2023; Accepted: 25.11.2023; First online: 12.12.2023

For citation. Parovik R. I. Fractional model of geoacoustic emission. Vestnik KRAUNC. Fiz.-mat. nauki. 2023, 45: 4, 24-35. EDN: CJMOVH.

Funding. 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»

Competing interests. There are no conflicts of interest regarding authorship and publication.

Contribution and Responsibility. The author participated in the writing of the article and is fully responsible for submitting the final version of the article to the press.

^\astCorrespondence: E-mail:

The content is published under the terms of the Creative Commons Attribution 4.0 International License

© Parovik R. I., 2023

© Institute of Cosmophysical Research and Radio Wave Propagation, 2023 (original layout, design, compilation)


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Information about author

Parovik Roman Ivanovich – D. Sci. (Phys. & Math.), Associate Professor, Leading researcher laboratory of modeling physical processes Institute of Cosmophysical Research and Radio Wave Propagation FEB RAS, Paratunka, Russia, ORCID 0000-0002-1576-1860.