# A numerical method for solving fractional optimal control problems using the operational matrix of Mott polynomials

Document Type : Research Paper

Authors

1 Department of Mathematics, Payame Noor University, Tehran, Iran.

2 Department of Mathematics, Technical and Vocational University, Tehran, Iran.

3 Department of Mathematics, Payame Noor University, PO BOX 19395-3697, Tehran, Iran.

Abstract

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 used the approach to approximate the state and control functions by the Mott polynomials (M-polynomials). We introduced the operational matrix of fractional Riemann-Liouville integration and apply it to approximate the fractional derivative of the basis. We investigated the convergence of the new method and some examples are included to demonstrate the validity and applicability of the proposed method.

Keywords

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### History

• Receive Date: 27 April 2020
• Revise Date: 22 April 2021
• Accept Date: 01 May 2021
• First Publish Date: 01 May 2021