A hybrid method for variable-order fractional 2D optimal control problems on an unbounded domain

In this study, the Caputo-Fabrizio fractional derivative is applied to generate a new category of variable-order fractional 2D optimization problems in an unbounded domain. To approach this problem, a novel hybrid method is devised which simultaneously exploits two sets of basis functions: a new class of basis functions namely the modified second kind Chebyshev functions and the shifted second kind Chebyshev cardinal functions. With the aid of the Lagrange multipliers method, the presented method converts the optimization problem under study into a system of algebraic equations, which are uncomplicated to solve. To confirm the precision of this new hybrid method, a convincing number of test problems are examined.