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Vestnik KRAUNC. Fiz.-Mat. Nauki, 2016, Number 2(13), Pages 43–49 (Mi vkam130)  

This article is cited in 1 scientific paper (total in 1 paper)

MATHEMATICAL MODELING

Mathematical modeling of nonlinear oscillators hereditarity example Duffing oscillator with fractional derivatives in the Riemann-Liouville

I. V. Drobysheva

Vitus Bering Kamchatka State University, 683031, Petropavlovsk-Kamchatsky, Pogranichnaya st., 4, Russia

Abstract: The paper presents a mathematical model hereditarity Duffing oscillator with friction, which is a generalization of previously known classical model of Duffing oscillator. This generalization is replaced in the model equation integral derivative on derivatives of fractional order in the sense of Riemann-Liouville. Built explicit finite difference scheme for calculating approximate solutions, as well as the phase trajectories for different values of the control parameters.

Keywords: Riemann-Liouville derivative Grunwald-Letnikova, hereditarity, Duffing oscillator, phase trajectory.

DOI: https://doi.org/10.18454/2079-6641-2016-13-43-49

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English version:
Bulletin KRASEC. Physical and Mathematical Sciences, 2016, 13:2, 39–45

Bibliographic databases:

UDC: 517. 925.42
MSC: 34C26
Received: 18.03.2016

Citation: I. V. Drobysheva, “Mathematical modeling of nonlinear oscillators hereditarity example Duffing oscillator with fractional derivatives in the Riemann-Liouville”, Vestnik KRAUNC. Fiz.-Mat. Nauki, 2016, no. 2(13), 43–49; Bulletin KRASEC. Phys. & Math. Sci., 13:2 (2016), 39–45

Citation in format AMSBIB
\Bibitem{Dro16}
\by I.~V.~Drobysheva
\paper Mathematical modeling of nonlinear oscillators hereditarity example Duffing oscillator with fractional derivatives in the Riemann-Liouville
\jour Vestnik KRAUNC. Fiz.-Mat. Nauki
\yr 2016
\issue 2(13)
\pages 43--49
\mathnet{http://mi.mathnet.ru/vkam130}
\crossref{https://doi.org/10.18454/2079-6641-2016-13-43-49}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3535556}
\elib{http://elibrary.ru/item.asp?id=26527428}
\transl
\jour Bulletin KRASEC. Phys. & Math. Sci.
\yr 2016
\vol 13
\issue 2
\pages 39--45
\crossref{https://doi.org/10.18454/2313-0156-2016-13-2-39-45}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. E. R. Novikova, “Ostsillyator Van-der-Polya–Duffinga c effektom ereditarnosti”, Vestnik KRAUNTs. Fiz.-mat. nauki, 2017, no. 2(18), 65–75  mathnet  crossref  elib
  • Vestnik KRAUNC. Fiziko-Matematicheskie Nauki Vestnik KRAUNC. Fiziko-Matematicheskie Nauki
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