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Russian Physics Journal

, Volume 61, Issue 8, pp 1410–1417 | Cite as

Variational Interpolation of Solutions of Fractional Differential Equations

  • V. A. Litvinov
Article
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Objects of research are fractional order differential equations of mathematical physics, and subject of research is the application of the variational interpolation method for solving such equations. The procedure of variational interpolation is stated, and its application to a solution of the simplest fractional order differential equations is demonstrated. It is shown that the approximate solutions constructed on two basic solutions of integer order equations have an error less than 10% for variables changing in a wide range, and in certain cases coincide with exact solutions.

Keywords

fractional derivatives numerical methods variational interpolation 

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References

  1. 1.
    S. Yu. Lukashuk, Analytical methods and numerical algorithms of investigation of fractional-differential mathematical diffusion-type models, Doctoral Thesis in Physical and Mathematical Sciences, Ufa State Aviation Technical University, Ufa (2017).Google Scholar
  2. 2.
    V. V. Uchaikin, Method of Fractional Derivatives [in Russian], Artishok, Ulyanovsk (2008).Google Scholar
  3. 3.
    S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Order Integrals and Derivatives and Their Applications [in Russian], Nauka i Tekhnika, Minsk (1987).Google Scholar
  4. 4.
    L. Changpin and Z. Fanhai, Numerical Methods for Fractional Calculus, Taylor & Francis Group (2015).Google Scholar
  5. 5.
    V. V. Uchaikin, Atomn. Energ., 67, 54–55 (1989).Google Scholar
  6. 6.
    V. V. Uchaikin and V. A. Litvinov, Opt. Atm. Okeana, 2, 36–40 (1989).Google Scholar
  7. 7.
    V. A. Litvinov, Yad. Fiz., 56, No. 2, 244–254 (1993).Google Scholar
  8. 8.
    A. A. Lagutin, V. A. Litvinov, and V. V. Uchaikin, Sensitivity Theory in Physics of Cosmic Rays [in Russian], Publishing House of Altai State University, Barnaul (1995).Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Barnaul Law Institute of the Ministry of Internal Affairs of RussiaBarnaulRussia

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