Abstract
We construct the solution of the fractional space-time equations that describe the vibrations of a quasi-one-dimensional fractal elastic string. We give the solution of the Cauchy problem for fractional differential equations with initial conditions. We carry out a numerical analysis and construct the graphic variation of the displacement function of a fractal elastic string. Three figures. Bibliography: 7 titles.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature Cited
R. R. Nigmattulin,Theoret. Mat. Fiz.,90, No. 3, 354–368 (1992).
B. B. Mandelbrot,The Fractal Geometry of Nature, New York (1982).
S. G. Samko, A. A. Kilbas, and O. I. Marichev,Integrals and Derivatives of Fractional Order and Certain of their Applications [in Russian], Minsk (1987).
V. Abramov, and O. Abramova, “Fractional space-time equations of fractal elastic matter,” in:Proceedings of the All-union Conference on ‘Development and Application of Mathematical Methods in Scientific Research’ [in Ukrainian], L'viv (1995), Part 2, pp. 62–63.
O. P. Abramova and N. O. Dmitrenko, “Modeling the vibrations of a fractal elastic string,” in:Proceedings of the Ukrainian Conference on ‘Modeling and Study of Elastic Systems’ [in Russian], Kiev (1996), p. 2.
V. S. Abramov and O. P. Abramova, “The introduction of fractal elastic media into the theory of dynamics on the basis of the fractional calculus,”J. Electrotech. Math.,1, 1–8 (1996).
H. Bateman, and A. Erdelyi,Higher Transcendental Functions, McGraw-Hill, New York (1953–55.
Additional information
Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 26, 1996, pp. 142–147
Rights and permissions
About this article
Cite this article
Abramova, O.P., Efimenko, N.O. Vibrations of a fractal elastic string. J Math Sci 86, 3176–3179 (1997). https://doi.org/10.1007/BF02355722
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02355722