Collocation method for solving nonlinear fractional optimal control problems by using Hermite scaling function with error estimates

This article presents an efficient numerical method for solving fractional optimal control problems (FOCPs) by utilizing the Hermite scaling function operational matrix of fractional-order integration. The proposed technique is applied to transform the state and control variables into nonlinear programming (NLP) parameters at collocation points. The NLP solver is then used to solve FOCP. Furthermore, theL(2)-error estimates in the approximation of unknown variables and the approximation of block pulse operational matrix of fractional-order integration are derived and illustrative examples are included to demonstrate the applicability of the proposed method. Moreover, the results are compared with the Haar wavelet collocation method, hybrid of block-pulse and Taylor polynomials method, Bernstein polynomials method, and the Boubaker hybrid function method to show the superiority of the proposed method.