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Features of the phase trajectory of a fractal oscillator

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Abstract

Based on the solution of a system of differential equations of a fractional order α (1<α≤2), a solution for the so-called fractal oscillator is obtained. It is shown that the fractal oscillator solutions provide for the parametrization of a wide class of nonlinear processes.

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References

  1. B. B. Mandelbrot, The Fractal Geometry of Nature (Freeman, New York, 1982).

    Google Scholar 

  2. A. I. Olemskoi and A. Ya. Flat, Usp. Fiz. Nauk 163(12), 1 (1993) [Phys. Usp. 36, 1087 (1993)].

    Google Scholar 

  3. V. V. Zosimov and L. M. Lyamshev, Usp. Fiz. Nauk 165(4), 361 (1995) [Phys. Usp. 38, 347 (1995)].

    Google Scholar 

  4. K. B. Oldham and J. Spanier, The Fractional Calculus: Theory and Application of Differentiation and Integration to Arbitrary Order (Academic, New York, 1974).

    Google Scholar 

  5. S. G. Samko, F. F. Kilbas, and O. I. Marichev, Integrals and Fractional-Order Derivatives and Some Applications (Nauka i Tekhnika, Minsk, 1987).

    Google Scholar 

  6. R. I. Nigmatulin, Teor. Mat. Fiz. 90(3), 354 (1992).

    Google Scholar 

  7. K. V. Chukbar, Zh. Éksp. Teor. Fiz. 108(5), 1875 (1995) [JETP 81, 1025 (1995)].

    Google Scholar 

  8. R. P. Meilanov, Pis’ma Zh. Tekh. Fiz. 22(23), 40 (1996) [Tech. Phys. Lett. 22, 967 (1996)].

    Google Scholar 

  9. R. P. Meilanov and S. A. Sadykov, Zh. Tekh. Fiz. 69(5), 128 (1999) [Tech. Phys. 44, 595 (1999)].

    Google Scholar 

  10. R. P. Meilanov, Inzh.-Fiz. Zh. 74(2), 34 (2001).

    Google Scholar 

  11. S. Lifshits, Geometric Theory of Differential Equations (Moscow, 1961).

  12. N. V. Butenin, Yu. I. Neimark, and N. A. Fufaev, An Introduction to the Theory of Nonlinear Oscillations (Nauka, Moscow, 1976).

    Google Scholar 

  13. N. N. Bogolyubov and Yu. A. Mitropol’skii, Asymptotic Methods in the Theory of Nonlinear Oscillations (Nauka, Moscow, 1974, 4th ed.; Gordon and Breach, New York, 1962).

    Google Scholar 

  14. J. K. Hale, Oscillations in Nonlinear Systems (McGraw-Hill, New York, 1963; Mir, Moscow, 1966).

    Google Scholar 

  15. N. N. Moiseev, Asymptotic Methods in Nonlinear Mechanics (Nauka, Moscow, 1981).

    Google Scholar 

  16. M. M. Dzharbashyan, Integral Transformations and Function Representations in Complex Domain (Nauka, Moscow, 1966).

    Google Scholar 

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Authors and Affiliations

  1. Institute for Problems of Geothermics, Dagestan Scientific Center, Russian Academy of Sciences, Makhachkala, Dagestan, Russia

    R. P. Meilanov & M. S. Yanpolov

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  1. R. P. Meilanov
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  2. M. S. Yanpolov
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__________

Translated from Pis’ma v Zhurnal Tekhnichesko\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) Fiziki, Vol. 28, No. 1, 2002, pp. 67–73.

Original Russian Text Copyright © 2002 by Me\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \)lanov, Yanpolov.

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Meilanov, R.P., Yanpolov, M.S. Features of the phase trajectory of a fractal oscillator. Tech. Phys. Lett. 28, 30–32 (2002). https://doi.org/10.1134/1.1448634

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  • DOI: https://doi.org/10.1134/1.1448634

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