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

Haleh Tajadodi; Hossein Jafari; Mahluli Naisbitt Ncube

doi:10.11121/ijocta.2022.1263

Authors

Haleh Tajadodi Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran https://orcid.org/0000-0001-8369-3698
Hossein Jafari Department of Mathematical Sciences, University of South Africa, UNISA0003, South Africa https://orcid.org/0000-0001-6807-6675
Mahluli Naisbitt Ncube Department of Mathematical Sciences, University of South Africa, UNISA0003, South Africa https://orcid.org/0000-0001-5060-8645

DOI:

https://doi.org/10.11121/ijocta.2022.1263

Keywords:

Fractional derivative, Optimal control problems, Operational matrix, Genocchi polynomials

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.

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Author Biographies

Haleh Tajadodi, Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran

is an assistant professor in the Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran. Her research interests include fractional differential equations, variational problems, approximation theory, and iterative methods.

Hossein Jafari, Department of Mathematical Sciences, University of South Africa, UNISA0003, South Africa

is a full professor in Applied Mathematics. His research interests include Bio-mathematics, fractional differential equations, Lie Symmetry, and approximation methods.

Mahluli Naisbitt Ncube, Department of Mathematical Sciences, University of South Africa, UNISA0003, South Africa

is a Ph.D. scholar at the Department of Mathematical Sciences, University of South Africa.

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