A Pseudospectral Method for Fractional Optimal Control Problems

In this article, a direct pseudospectral method based on Lagrange interpolating functions with fractional power terms is used to solve the fractional optimal control problem. As most applied fractional problems have solutions in terms of the fractional power, using appropriate characteristic nodal-based functions with suitable power leads to a more accurate pseudospectral approximation of the solution. The Lagrange interpolating functions and their fractional derivatives belong to the Müntz space; such functions are employed to show that a relationship exists between the Karush–Kukn–Tucker conditions associated with nonlinear programming and the first optimal necessary conditions. Furthermore, the convergence of the method is investigated. The obtained numerical results are an indication of the behavior of the algorithm.