Optimal Homotopy Asymptotic Method-Least Square for Solving Nonlinear Fractional-Order Gradient-Based Dynamic System from an Optimization Problem
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 formulat...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2020/8049397 |
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| author | Oluwaseun Olumide Okundalaye Wan Ainun Mior Othman Nallasamy Kumaresan |
| author_facet | Oluwaseun Olumide Okundalaye Wan Ainun Mior Othman Nallasamy Kumaresan |
| author_sort | Oluwaseun Olumide Okundalaye |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-a8e8af54eb764e44a487e391b8b437b7 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-a8e8af54eb764e44a487e391b8b437b72025-08-20T03:39:32ZengWileyAdvances in Mathematical Physics1687-91201687-91392020-01-01202010.1155/2020/80493978049397Optimal Homotopy Asymptotic Method-Least Square for Solving Nonlinear Fractional-Order Gradient-Based Dynamic System from an Optimization ProblemOluwaseun Olumide Okundalaye0Wan Ainun Mior Othman1Nallasamy Kumaresan2Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur, MalaysiaInstitute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur, MalaysiaInstitute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur, MalaysiaIn 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.http://dx.doi.org/10.1155/2020/8049397 |
| spellingShingle | Oluwaseun Olumide Okundalaye Wan Ainun Mior Othman Nallasamy Kumaresan Optimal Homotopy Asymptotic Method-Least Square for Solving Nonlinear Fractional-Order Gradient-Based Dynamic System from an Optimization Problem Advances in Mathematical Physics |
| title | Optimal Homotopy Asymptotic Method-Least Square for Solving Nonlinear Fractional-Order Gradient-Based Dynamic System from an Optimization Problem |
| title_full | Optimal Homotopy Asymptotic Method-Least Square for Solving Nonlinear Fractional-Order Gradient-Based Dynamic System from an Optimization Problem |
| title_fullStr | Optimal Homotopy Asymptotic Method-Least Square for Solving Nonlinear Fractional-Order Gradient-Based Dynamic System from an Optimization Problem |
| title_full_unstemmed | Optimal Homotopy Asymptotic Method-Least Square for Solving Nonlinear Fractional-Order Gradient-Based Dynamic System from an Optimization Problem |
| title_short | Optimal Homotopy Asymptotic Method-Least Square for Solving Nonlinear Fractional-Order Gradient-Based Dynamic System from an Optimization Problem |
| title_sort | optimal homotopy asymptotic method least square for solving nonlinear fractional order gradient based dynamic system from an optimization problem |
| url | http://dx.doi.org/10.1155/2020/8049397 |
| work_keys_str_mv | AT oluwaseunolumideokundalaye optimalhomotopyasymptoticmethodleastsquareforsolvingnonlinearfractionalordergradientbaseddynamicsystemfromanoptimizationproblem AT wanainunmiorothman optimalhomotopyasymptoticmethodleastsquareforsolvingnonlinearfractionalordergradientbaseddynamicsystemfromanoptimizationproblem AT nallasamykumaresan optimalhomotopyasymptoticmethodleastsquareforsolvingnonlinearfractionalordergradientbaseddynamicsystemfromanoptimizationproblem |