A Robust Galerkin Fractional Taylor Technique to Solve Multi-Dimensional Fractional Optimal Control Problems with Inequality Constraints

A new computational approach is presented for solving MFOCPs subject to Caputo fractional dynamics by means of Galerkin projection technique along with fractional Taylor polynomial expansions. The method successfully deals with constraints in the form of both equalities and inequalities. An important feature of the new method includes deriving an operational matrix based on fractional Taylor polynomials such that, using the Galerkin approach, the problem under study is reduced to a set of algebraic equations. Convergence analysis of the Taylor series expansions is investigated in detail. The performance of the approach is confirmed by applying it to four problems in comparison with other existing approaches in the literature. MSC 2010: 49M05; 65T60