Approximate Technique for Solving Class of Fractional Variational Problems

Emad M. Solouma^1,2, Mohamed M. Khader^1,3

¹Department of Mathematics and Statistics, College of Science, Al-Imam Mohammad Ibn Saud Islamic, University (IMSIU), Riyadh, Saudi Arabia.
²Department of Mathematics, College of Science, Beni-Suef University, Beni-Suef, Egypt.
³Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt.

DOI: 10.4236/am.2015.65078                

Abstract

This paper is devoted to implementing the Legendre spectral collocation method to introduce numerical solutions of a certain class of fractional variational problems (FVPs). The properties of the Legendre polynomials and Rayleigh-Ritz method are used to reduce the FVPs to the solution of system of algebraic equations. Also, we study the convergence analysis. The obtained numerical results show the simplicity and the efficiency of the proposed method.

Keywords

Fractional Variational Problems, Caputo Fractional Derivatives, Legendre Spectral Collocation Method, Rayleigh-Ritz Method, Convergence Analysis

Conflicts of Interest

The authors declare no conflicts of interest.

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