Novel operational matrices for solving 2-dim nonlinear variable order fractional optimal control problems via a new set of basis functions

This paper provides an effective method for a class of 2-dim nonlinear variable order fractional optimal control problems (2DNVOFOCP). The technique is based on the new class of basis functions namely the generalized shifted Legendre polynomials. The dynamic constraint is described by a nonlinear variable order fractional differential equation where the fractional derivative is in the sense of Caputo. The 2-dim Gauss-Legendre quadrature rule together with the Lagrange multipliers method are utilized to find the solutions of the given 2DNVOFOCP. The convergence analysis of the presented method is investigated. The examined numerical examples manifest highly accurate results.