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)
F. Ahmed, Hoda and B. Melad, Marina
"A New Approach for Solving Fractional Optimal Control Problems Using Shifted Ultraspherical Polynomials,"
Progress in Fractional Differentiation & Applications: Vol. 4
, Article 3.
Available at: https://dc.naturalspublishing.com/pfda/vol4/iss3/3