New Numerical Approach for Fractional Variational Problems Using Shifted Legendre Orthonormal Polynomials

Samer S. Ezz-Eldien (), Ramy M. Hafez (), Ali H. Bhrawy (), Dumitru Baleanu () and Ahmed A. El-Kalaawy ()
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Samer S. Ezz-Eldien: Assiut University
Ramy M. Hafez: Modern Academy
Ali H. Bhrawy: Beni-Suef University
Dumitru Baleanu: Çankaya University
Ahmed A. El-Kalaawy: Beni-Suef University

Journal of Optimization Theory and Applications, 2017, vol. 174, issue 1, No 19, 295-320

Abstract: Abstract This paper reports a new numerical approach for numerically solving types of fractional variational problems. In our approach, we use the fractional integrals operational matrix, described in the sense of Riemann–Liouville, with the help of the Lagrange multiplier technique for converting the fractional variational problem into an easier problem that consisting of solving an algebraic equations system in the unknown coefficients. Several numerical examples are introduced, combined with their approximate solutions and comparisons with other numerical approaches, for confirming the accuracy and applicability of the proposed approach.

Keywords: Fractional variational problems; Lagrange multiplier technique; Riemann–Liouville integrals; Operational matrix; Legendre polynomials; 34A08; 65M70; 33C45 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-016-0886-1

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