A new operational matrix based on Boubaker wavelet for solving optimal control problems of arbitrary order

This paper presents numerical solution for solving the nonlinear one and two-dimensional optimal control problems of arbitrary order. First, we have constructed Boubaker wavelet for the first time and defined a general formulation for its fractional derivative operational matrix. To solve the one-dimensional problem, we have transformed the problems into an optimization one. The similar process together with the Ritz method are applied to find a solution for two-dimensional problems as well. Then, the necessary conditions of optimality result in a system of algebraic equations with unknown coefficients and then control parameters can be simply solved. The error vector is considered to show the convergence of the used approximation in this method. Finally, some illustrative examples are given to demonstrate accuracy and efficiency of the proposed method.