An approach to solve fractional optimal control problems via fractional-order Boubaker wavelets

This work is devoted to numerical solution to solve fractional optimal control problems (FOCPs). The fractional-order Boubaker wavelets (FOBWs) are introduced. By applying hypergeometric functions, an exact formula for Riemann–Liouville fractional integral operator for FOBW is obtained. By using this formula, the FOCP is reduced into a corresponding optimization problem which can be solved by applying the Lagrange multiplier method. Also, the convergence for the present method is provided. Seven numerical examples are included to demonstrate the applicability of the proposed technique. In Example 6, it will be shown that we can achieve the exact solutions which were not obtained previously in the literature. In addition, in Example 7, a practical example in a cancer model is provided.