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Fractional variational problems; Bernstein polynomials; Rayleigh–Ritz method.

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.

HALEH TAJADODI¹ NEMATOLLAH KADKHODA² HOSSEIN JAFARI^{3 4} MUSTAFA INC^{5 6}

1. Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran
2. Department of Mathematics, Faculty of Basic Sciences, Bozorgmehr University of Qaenat, Qaenat, Iran
3. Department of Mathematics, University of Mazandaran, Babolsar, Iran
4. Department of Mathematical Sciences, University of South Africa (UNISA), P.O. Box 392, Pretoria 0003, South Africa
5. Department of Mathematics, Firat University, Elazig 23119, Turkey
6. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

Published

13 October 2020

Manuscript received

28 January 2020

Manuscript revised

12 May 2020

Accepted

1 July 2020

Final version published online

13 October 2020