A new optimal homotopy asymptotic method for fractional optimal control problems
Solving fractional optimal control problems (FOCPs) with an approximate analytical method has been widely studied by many authors, but to guarantee the convergence of the series solution has been a challenge. We solved this by integrating the Galerkin method of optimization technique into the whole...
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my.um.eprints.348372022-09-07T04:04:41Z http://eprints.um.edu.my/34837/ A new optimal homotopy asymptotic method for fractional optimal control problems Okundalaye, Oluwaseun Olumide Othman, Wan Ainun Mior QA Mathematics Solving fractional optimal control problems (FOCPs) with an approximate analytical method has been widely studied by many authors, but to guarantee the convergence of the series solution has been a challenge. We solved this by integrating the Galerkin method of optimization technique into the whole region of the governing equations for accurate optimal values of control-convergence parameters C-j(s). The arbitrary-order derivative is in the conformable fractional derivative sense. We use Euler-Lagrange equation form of necessary optimality conditions for FOCPs, and the arising fractional differential equations (FDEs) are solved by optimal homotopy asymptotic method (OHAM). The 011AM technique speedily provides the convergent approximate analytical solution as the arbitrary order derivative approaches 1. The convergence of the method is discussed, and its effectiveness is verified by some illustrative test examples. Hindawi Ltd 2021-05-15 Article PeerReviewed Okundalaye, Oluwaseun Olumide and Othman, Wan Ainun Mior (2021) A new optimal homotopy asymptotic method for fractional optimal control problems. International Journal of Differential Equations, 2021. ISSN 1687-9643, DOI https://doi.org/10.1155/2021/6633130 <https://doi.org/10.1155/2021/6633130>. 10.1155/2021/6633130 |
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QA Mathematics Okundalaye, Oluwaseun Olumide Othman, Wan Ainun Mior A new optimal homotopy asymptotic method for fractional optimal control problems |
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Solving fractional optimal control problems (FOCPs) with an approximate analytical method has been widely studied by many authors, but to guarantee the convergence of the series solution has been a challenge. We solved this by integrating the Galerkin method of optimization technique into the whole region of the governing equations for accurate optimal values of control-convergence parameters C-j(s). The arbitrary-order derivative is in the conformable fractional derivative sense. We use Euler-Lagrange equation form of necessary optimality conditions for FOCPs, and the arising fractional differential equations (FDEs) are solved by optimal homotopy asymptotic method (OHAM). The 011AM technique speedily provides the convergent approximate analytical solution as the arbitrary order derivative approaches 1. The convergence of the method is discussed, and its effectiveness is verified by some illustrative test examples. |
format |
Article |
author |
Okundalaye, Oluwaseun Olumide Othman, Wan Ainun Mior |
author_facet |
Okundalaye, Oluwaseun Olumide Othman, Wan Ainun Mior |
author_sort |
Okundalaye, Oluwaseun Olumide |
title |
A new optimal homotopy asymptotic method for fractional optimal control problems |
title_short |
A new optimal homotopy asymptotic method for fractional optimal control problems |
title_full |
A new optimal homotopy asymptotic method for fractional optimal control problems |
title_fullStr |
A new optimal homotopy asymptotic method for fractional optimal control problems |
title_full_unstemmed |
A new optimal homotopy asymptotic method for fractional optimal control problems |
title_sort |
new optimal homotopy asymptotic method for fractional optimal control problems |
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Hindawi Ltd |
publishDate |
2021 |
url |
http://eprints.um.edu.my/34837/ |
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1744649198109720576 |
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13.18916 |