Introducing the infinite world of the OPERATIONAL Matrix

This paper presents a numerical method for solving a class of fractional optimal control problems (FOCPs) based on numerical polynomial approximation. The fractional derivative in the dynamic system is described in the Caputo sense. We applied the approach in order to approximate the state and control functions by the Mott polynomials (M-polynomials), then introduced the operational matrix of fractional Riemann-Liouville integration and apply it to approximate fractional derivative of the basis. Finally, investigated the convergence of the new method and some examples are included to demonstrate the validity and applicability of the proposed method.

Keywords:

Fractional optimal control problem , Caputo derivative , Mott polynomials basis , Operational matrix.