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Approximate technique for solving fractional variational problems

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Abstract

The purpose of this paper is to suggest a numerical technique to solve fractional variational problems (FVPs). These problems are based on Caputo fractional derivatives. Rayleigh–Ritz method is used in this technique. First we approximate the objective function by the trapezoidal rule. Then, the unknown function is expanded in terms of the Bernstein polynomials. By this method, a system of algebraic equations is driven. We provide examples to show the effectiveness of this technique, which is considered in the current study.

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Authors and Affiliations

  1. Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran

    Haleh Tajadodi

  2. Department of Mathematics, Faculty of Basic Sciences, Bozorgmehr University of Qaenat, Qaenat, Iran

    Nematollah Kadkhoda

  3. Department of Mathematics, University of Mazandaran, Babolsar, Iran

    Hossein Jafari

  4. Department of Mathematical Sciences, University of South Africa (UNISA), P.O. Box 392, Pretoria, 0003, South Africa

    Hossein Jafari

  5. Department of Mathematics, Firat University, Elazig, 23119, Turkey

    Mustafa Inc

  6. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

    Mustafa Inc

Authors
  1. Haleh Tajadodi
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  2. Nematollah Kadkhoda
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  3. Hossein Jafari
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  4. Mustafa Inc
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Correspondence to Mustafa Inc.

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Tajadodi, H., Kadkhoda, N., Jafari, H. et al. Approximate technique for solving fractional variational problems. Pramana - J Phys 94, 146 (2020). https://doi.org/10.1007/s12043-020-02004-w

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  • DOI: https://doi.org/10.1007/s12043-020-02004-w

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