Bulletin KRASEC. Phys. & Math. Sci. 2016. V. 13. no. 2. pp. 46-49. ISSN 2313-0156
DOI: 10.18454/2313-0156-2016-13-2-46-49
MSC 34C26
DUFFING OSCILLATOR WITH EXTERNAL HARMONIC ACTION AND VARIABLE FRACTIONAL RIEMANN-LIOUVILLE DERIVATIVE CHARACTERIZING VISCOUS FRICTION
V. A. Kim
Vitus Bering Kamchatka State University, 683031, Petropavlovsk-Kamchatsky, Pogranichnaya st., 4, Russia
E-mail: valentinekim93@mail.ru
The paper suggested generalization of Duffing oscillator with viscous hereditary friction which is represented by the operator of a variable fractional derivative in the sense of Riemann-Liouville. Explicit finite-difference scheme was derived to calculate approximate solutions, and phase trajectories for different values of control parameters were plotted.
Key words: Riemann-Liouville derivative, Grunwald-Letnikov derivative, heredity, Duffing oscillator, phase trajectory.
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For citation: Kim V. A. Duffing oscillator with external harmonic action and variable fractional Riemann-Liouville derivative characterizing viscous friction. Bulletin KRASEC. Physical and Mathematical Sciences 2016, vol. 13, no 2, 46-49. DOI: 10.18454/2313-0156-2016-13-2-46-49.
Original article submitted: 16.04.2016
Kim Valentin Aleksandrovich – fourthyear student training direction «Applied Mathematics and Informatics», Kamchatka Vitus Bering State University, Petropavlovsk- Kamchatsky, Russia.
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