Numerical study of nonlinear 2D optimal control problems with multi-term variable-order fractional derivatives in the Atangana-Baleanu-Caputo sense

Abstract

Abstract This paper introduces a new category of nonlinear 2D optimal control problems (OPCs) with multi-term variable-order (V-O) fractional derivatives in their dynamical systems. The fractional derivatives are considered in the sense of Atangana-Baleanu-Caputo. A computational procedure based on the Chebyshev cardinal functions (CCFs) and the Lagrange multipliers technique is developed for the approximate solution of such problems. The presented method simplify these complex problems by expanding the state and control functions in terms of the CCFs. The applicability of the formulated approach is investigated through forth numerical examples. The obtained results manifest the high precision of the proposed algorithm.