AccScience Publishing / IJOCTA / Volume 12 / Issue 2 / DOI: 10.11121/ijocta.2022.1263
RESEARCH ARTICLE

Genocchi polynomials as a tool for solving a class of fractional optimal control problems

Haleh Tajadodi1 Hossein Jafari2* Mahluli Naisbitt Ncube2
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1 Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran
2 Department of Mathematical Sciences, University of South Africa, UNISA0003, South Africa
IJOCTA 2022, 12(2), 160–168; https://doi.org/10.11121/ijocta.2022.1263
Submitted: 1 May 2022 | Accepted: 24 July 2022 | Published: 27 July 2022
© 2022 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
Abstract

In this research, we use operational matrix based on Genocchi polynomials to obtain approximate solutions for a class of fractional optimal control problems. The approximate solution takes the form of a product consisting of unknown coefficients and the Genocchi polynomials. Our main task is to compute the numerical values of the unknown coefficients. To achieve this goal, we apply the initial condition of the problem, the Tau and Lagrange multiplier methods. We do error analysis as a means to study the behaviour of the approximate solutions.

Keywords
Fractional derivative
Optimal control problems
Genocchi polynomials
Operational matrix
Conflict of interest
The authors declare they have no competing interests.
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An International Journal of Optimization and Control: Theories & Applications, Electronic ISSN: 2146-5703 Print ISSN: 2146-0957, Published by AccScience Publishing