Geodesic
Mathematical modeling of nonlinear oscillators hereditarity example Duffing oscillator with fractional derivatives in the Riemann-Liouville
Vestnik KRAUNC. Fiziko-matematičeskie nauki, no. 2 (2016), pp. 43-49

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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. 
@article{VKAM_2016_2_a6,
     author = {I. V. Drobysheva},
     title = {Mathematical modeling of nonlinear oscillators hereditarity example {Duffing} oscillator with fractional derivatives in the {Riemann-Liouville}},
     journal = {Vestnik KRAUNC. Fiziko-matemati\v{c}eskie nauki},
     pages = {43--49},
     publisher = {mathdoc},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VKAM_2016_2_a6/}
}
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I. V. Drobysheva. Mathematical modeling of nonlinear oscillators hereditarity example Duffing oscillator with fractional derivatives in the Riemann-Liouville. Vestnik KRAUNC. Fiziko-matematičeskie nauki, no. 2 (2016), pp. 43-49. http://geodesic.mathdoc.fr/item/VKAM_2016_2_a6/