A New Optimal Homotopy Asymptotic Method for Fractional Optimal Control Problems. (15th May 2021)

• Record Type: Journal Article
• Authors: Okundalaye, Oluwaseun Olumide; Othman, Wan Ainun Mior
• Other Names: Ezzinbi Khalil Academic Editor.
• Is Part Of: International journal of differential equations. Volume 2021(2021)
• Publication Date: 2021-05-15
• Subjects: Differential equations -- Periodicals; Differential equations; Periodicals; 515.35
• DOI: 10.1155/2021/6633130
• Languages: English
• ISSNs: 1687-9643

Abstract

Abstract : 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 OHAM 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.