In this paper, we focus on the continuous-time nonlinear fractional
programming problems including the objective functional given by the ratio
of two integrals. Since the standard continuoustime programming theory, such
as optimal control theory, cannot be used directly to solve this type of
problems, we propose a new numerical method. At first we convert the
original problem into an equivalent continuous-time nonfractional problem
which does not include integral term. Then, we utilize a Legendre
pseudospectral method to discretize the gained problem. We also analyze the
feasibility of the obtained discretized problem and the convergence of the
method. Finally, we provide two numerical examples to demonstrate the
efficiency and capability of the method.