"A New Approach for Solving Fractional Optimal Control Problems Using S" by Hoda F. Ahmed and Marina B. Melad

Progress in Fractional Differentiation & Applications

Article Title

A New Approach for Solving Fractional Optimal Control Problems Using Shifted Ultraspherical Polynomials

Authors

Hoda F. Ahmed, Department of Mathematics, Faculty of Science, Minia University, Minia, Egypt
Marina B. Melad

Author Country (or Countries)

Egypt

Abstract

We propose a numerical scheme for solving the one- and two-dimensional fractional optimal control problems (FOCPs). The suggested scheme is established by using the operational matrix (OM) of the Riemann-Liouville fractional integral (RLFI) of the shifted Gegenbauer polynomials (SGPs). These polynomials generalize the shifted Legendre and shifted Chebyshev polynomials, and are special cases of the Jacobi polynomials. By employing the proposed technique, the FOCP is converted into a variational problem. The Gegenbauer- Gauss quadrature method (GGQM) and the Rayleigh-Ritz method (RRM) are implemented to convert the obtained variational problem into a system of algebraic equations (AEs) which is easy to solve. Numerical results of some examples including the one- and two-dimensional FOCPs are shown to prove the validity of the investigated technique.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/pfda/040303

Recommended Citation

F. Ahmed, Hoda and B. Melad, Marina (2018) "A New Approach for Solving Fractional Optimal Control Problems Using Shifted Ultraspherical Polynomials," Progress in Fractional Differentiation & Applications: Vol. 4: Iss. 3, Article 3.
DOI: http://dx.doi.org/10.18576/pfda/040303
Available at: https://digitalcommons.aaru.edu.jo/pfda/vol4/iss3/3

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