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News of the Kabardino-Balkarian Scientific Center of the Russian Academy of Sciences, 2020, Issue 1, Pages 46–56
DOI: https://doi.org/10.35330/1991-6639-2020-1-93-46-56 (Mi izkab101) 		 
This article is cited in 2 scientific papers (total in 2 papers)

PHYSICAL-MATHEMATICAL SCIENCES

Investigation of forced oscillations of a Duffing oscillator with a variable fractional order derivative

V. A. Kimabc, R. I. Parovikad

a Vitus Bering Kamchatka State University, 683032, Petropavlovsk-Kamchatsky, Pogranichnaya street, 4
b Institute of Applied Mathematics and Automation – branch of the FSBSE "Federal Scientific Center "Kabardin-Balkar Scientific Center of the Russian Academy of Sciences", 360000, KBR, Nalchik, Shortanov street, 89 A
c Kamchatka State Technical University, 683003, Petropavlovsk-Kamchatsky, st. Klyuchevskaya, 35
d Institute of Cosmophysical Research and Radio Wave Propagation FEB RAS, 684034, Kamchatka Territory, Yelizovsky District, v. Paratunka, Mirnaya street, 7
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DOI: https://doi.org/10.35330/1991-6639-2020-1-93-46-56
Abstract: A mathematical model of a Duffing type oscillator with a variable fractional derivative of the Riemann-Liouville derivative is studied. Using the harmonic balance method, algorithms for constructing amplitude-phase characteristics were found. The amplitude-frequency and phase-frequency characteristics were built. The inverse dependence of the Q factor on the order of the fractional derivative is shown. The Q-factor surfaces are constructed depending on the frequency and amplitude.
Keywords: Riemann-Liouville derivative, Grunwald-Letnikov derivative, oscillograms, phase trajectories, amplitude-frequency characteristic (AFC), phase-frequency characteristic (PFC).
Funding agency Grant number
Russian Foundation for Basic Research 19-31-50033
This work was supported by the Russian Foundation for Basic Research (project No. 19-31-50033).
Received: 11.02.2020
Bibliographic databases:
Document Type: Article
UDC: 517.98; 517.2
Language: Russian
Citation: V. A. Kim, R. I. Parovik, “Investigation of forced oscillations of a Duffing oscillator with a variable fractional order derivative”, News of the Kabardino-Balkarian Scientific Center of the Russian Academy of Sciences, 2020, no. 1, 46–56
Citation in format AMSBIB
\Bibitem{KimPar20}
\by V.~A.~Kim, R.~I.~Parovik
\paper Investigation of forced oscillations
of a Duffing oscillator with a variable
fractional order derivative
\jour News of the Kabardino-Balkarian Scientific Center of the Russian Academy of Sciences
\yr 2020
\issue 1
\pages 46--56
\mathnet{http://mi.mathnet.ru/izkab101}
\crossref{https://doi.org/10.35330/1991-6639-2020-1-93-46-56}
\elib{https://elibrary.ru/item.asp?id=https://www.elibrary.ru/item.asp?id=42622685}
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