Müntz–Legendre wavelet method for solving Sturm–Liouville fractional optimal control problem with error estimates

Abstract

SummaryThis paper develops a Müntz–Legendre wavelet method for solving a fractional optimal control problem with dynamic constraint as a fractional Sturm–Liouville problem. We first derive the necessary optimality conditions as a two‐point boundary value problem by using the calculus of variation and integration by part formula. The operational matrices for Müntz–Legendre scaling functions have been obtained, and by utilizing it, the two‐point boundary value problem has been converted into a system of algebraic equations. The ‐error estimates in the approximation of operations matrices and in the approximation of unknown variable by the Müntz–Legendre wavelet has been derived. In the last, illustrative examples have been taken to show the applicability of the proposed method.