Geodesic
Fractional model of geoacoustic emission
Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 45 (2023) no. 4, pp. 24-35 Cet article a éte moissonné depuis la source Math-Net.Ru

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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, phase trajectory, explicit finite-difference, Maple.
Mots-clés : geoacoustic emissions, oscillogram 
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R. I. Parovik. Fractional model of geoacoustic emission. Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 45 (2023) no. 4, pp. 24-35. http://geodesic.mathdoc.fr/item/VKAM_2023_45_4_a1/

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