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

Author

Listed:
  • Samer S. Ezz-Eldien

    (Assiut University)

  • Ramy M. Hafez

    (Modern Academy)

  • Ali H. Bhrawy

    (Beni-Suef University)

  • Dumitru Baleanu

    (Çankaya University
    Institute of Space Sciences)

  • Ahmed A. El-Kalaawy

    (Beni-Suef University)

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.

Suggested Citation

  • Samer S. Ezz-Eldien & Ramy M. Hafez & Ali H. Bhrawy & Dumitru Baleanu & Ahmed A. El-Kalaawy, 2017. "New Numerical Approach for Fractional Variational Problems Using Shifted Legendre Orthonormal Polynomials," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 295-320, July.
    • Handle: RePEc:spr:joptap:v:174:y:2017:i:1:d:10.1007_s10957-016-0886-1
    DOI: 10.1007/s10957-016-0886-1
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    References listed on IDEAS

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    1. Ahmad, Wajdi M. & El-Khazali, Reyad, 2007. "Fractional-order dynamical models of love," Chaos, Solitons & Fractals, Elsevier, vol. 33(4), pages 1367-1375.
    2. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    3. James W. Kirchner & Xiahong Feng & Colin Neal, 2000. "Fractal stream chemistry and its implications for contaminant transport in catchments," Nature, Nature, vol. 403(6769), pages 524-527, February.
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    Cited by:

    1. Fakhrodin Mohammadi & Hossein Hassani, 2019. "Numerical Solution of Two-Dimensional Variable-Order Fractional Optimal Control Problem by Generalized Polynomial Basis," Journal of Optimization Theory and Applications, Springer, vol. 180(2), pages 536-555, February.
    2. Harendra Singh & Rajesh K. Pandey & Hari Mohan Srivastava, 2019. "Solving Non-Linear Fractional Variational Problems Using Jacobi Polynomials," Mathematics, MDPI, vol. 7(3), pages 1-24, February.

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