Numerical solution a class of 2D fractional optimal control problems by using 2D Muntz-Legendre wavelets

In this paper, a method for finding an approximate solution of a class of 2D fractional optimal control problems with fractional-order dynamical system is discussed. In the proposed method, the fractional derivative is expressed in the Caputo sense. The method consists of expanding unknown functions as the elements of two-dimensional (2D) Muntz-Legendre wavelets. The 2D Muntz-Legendre wavelets are constructed and their properties are presented. The operational matrix of fractional-order integration for these wavelets is utilized to reduce the solution of 2D fractional optimal control problem to an optimization problem, which can then be solved easily. Some results concerning the error analysis are obtained. Finally, two illustrative test problems are included to demonstrate the validity and applicability of the technique. Moreover, our achievements are compared with the previous results to show the superiority of the proposed method.