# Optimal Homotopy Asymptotic Method-Least Square for Solving Nonlinear Fractional-Order Gradient-Based Dynamic System from an Optimization Problem

Okundalaye, Oluwaseun Olumide and Othman, Wan Ainun Mior and Kumaresan, Nallasamy (2020) Optimal Homotopy Asymptotic Method-Least Square for Solving Nonlinear Fractional-Order Gradient-Based Dynamic System from an Optimization Problem. Advances in Mathematical Physics, 2020. p. 8049397. ISSN 1687-9120, DOI https://doi.org/10.1155/2020/8049397.

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Official URL: https://doi.org/10.1155/2020/8049397

## Abstract

In this paper, we consider an approximate analytical method of optimal homotopy asymptotic method-least square (OHAM-LS) to obtain a solution of nonlinear fractional-order gradient-based dynamic system (FOGBDS) generated from nonlinear programming (NLP) optimization problems. The problem is formulated in a class of nonlinear fractional differential equations, (FDEs) and the solutions of the equations, modelled with a conformable fractional derivative (CFD) of the steepest descent approach, are considered to find the minimizing point of the problem. The formulation extends the integer solution of optimization problems to an arbitrary-order solution. We exhibit that OHAM-LS enables us to determine the convergence domain of the series solution obtained by initiating convergence-control parameter Cj′s. Three illustrative examples were included to show the effectiveness and importance of the proposed techniques. © 2020 Oluwaseun Olumide Okundalaye et al.

Item Type: Article UNSPECIFIED Optimal homotopy asymptotic method-least square (OHAM-LS); fractional-order gradient-based dynamic system (FOGBDS); nonlinear programming (NLP) Q Science > Q Science (General)Q Science > QA Mathematics Faculty of Science > Institute of Mathematical Sciences Ms. Juhaida Abd Rahim 07 Sep 2020 00:46 07 Sep 2020 00:46 http://eprints.um.edu.my/id/eprint/25502

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