Fractional optimal control using B-splines

In this paper, a direct spectral collocation method using B-spline functions is presented to approximate the solutions of fractional optimal control problems with inequality constraints. Applying these functions leads to sparse matrices because they have compact support, moreover, they produce a piecewise continuous solution. The method is based on approximating the control and Caputo fractional derivative of the state by B-spline functions. The fractional integral of these functions is computed using recurrence relations. The efficiency of the method has been shown using a numerical example.