Fractal Parametric Oscillator as a Model of a Nonlinear Oscillation System in Natural Mediums

Roman I. Parovik^{*}

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References

[1] A. M. Nakhushev, “Fractional Calculus and Its Application,” Fizmatlit, Moscow, 2003, p. 272.

[2] V. A. Gordeenko, “Vector-Phase Methods in Acoustics,” Fizmatlit, Moscow, 2007, p. 480.

[3] V. A. Nakhusheva, “Differential Equations of Mathematical Models of Non-Local Processes,” Nauka, Moscow, 2006, p. 173.

[4] R. P. Meilanov and M. S. Yanpolov, “Features of the Phase Trajectory of a Fractal Oscillator,” Technical Physics Letters, Vol. 28, No. 1, 2002, pp. 67-73.
doi:10.1134/1.1448634

[5] R. I. Parovik, “Cauchy Problem for Non Local Mathieu Equation,” Doklady AMAN, Vol. 13, No. 2, 2011, pp. 90-98.

[6] F. Van de Pol and M. J. Strutt, “On the Stability of the Solutions of Mathieu’s Equation,” Philosophical Magazine, Vol. 5, 1928, pp. 18-38.

[7] R. H. Rand, S. M. Sah and M. K. Suchrsky, “Fractional Mathieu Equation,” Communications in Nonlinear Science and Numerical Simulation, Vol. 15, 2010, pp. 3254-3262.

[8] V. V. Afanas’ev and M. J. E. Daniel, “Polish Stabilization of the Inertial Effects of the Fractal Oscillator,” Technical Physics Letters, Vol. 36, No. 7, 2010, pp. 1-6.