fractional 2d optimal control problems: numerical approach for solving

in this paper, a new method for solving twodimensional fractional optimal control problems (focp_s) based on the numerical polynomial approximation is stated. the approach is to estimate the unknown functions by the legendre orthonormal basis using the ritz method. then the twodimensional legendre-gauss (lg) quadrature rule is applied to approximate double integral of the performance index functional. next, the problem is converted into an equivalent nonlinear unconstrained minimization problem. finally, a test problem is included to show applicability of the new procedure.