Using Mott polynomials operational matrices to optimize multi-dimensional fractional optimal control problems

Abstract

We offer a method for solving the fractional optimal control problems of multi-dimensional. We obtain a fractional derivative and multiplication operational matrix for Mott polynomials (M-polynomials). In the proposed method, the Caputo sense of the fractional derivative is applied on dynamical system. The main feature of this method is to reduce the problem into a system of algebraic equations in order to simplify it. We also show that by increasing the approximation points, the responses converge to the real answer. When the degree of fractional derivative approaches to 1, then the obtained solution approaches to the classical solution as well.

Keywords

• mott polynomials
• caputo derivative
• fractional optimal control problems
• operational matrix