title: Numerical solution of some types of fractional optimal control problems.
abstract: We present two different approaches for the numerical solution of fractional optimal control problems (FOCPs) based on a spectral method using Chebyshev polynomials. The fractional derivative is described in the Caputo sense. The first approach follows the paradigm "optimize first, then discretize" and relies on the approximation of the necessary optimality conditions in terms of the associated Hamiltonian. In the second approach, the state equation is discretized first using the Clenshaw and Curtis scheme for the numerical integration of nonsingular functions followed by the Rayleigh-Ritz method to evaluate both the state and control variables. Two illustrative examples are included to demonstrate the validity and applicability of the suggested approaches.
authors.affiliation: Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt.
authors.forename: Nasser Hassan
authors.initials: NH
authors.lastname: Sweilam
authors.affiliation: Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt.
authors.forename: Tamer Mostafa
authors.initials: TM
authors.lastname: Al-Ajami
authors.affiliation: Institute of Mathematics, University of Augsburg, 86159 Augsburg, Germany ; Department of Mathematics, University of Houston, Houston, TX 77204-3008, USA.
authors.forename: Ronald H W
authors.initials: RH
authors.lastname: Hoppe