Study of fractional order Van der Pol equation
In this article, Homotopy analysis method is successfully used to find the approximate solution of fractional order Van der Pol equation. The fractional derivative is described in the Caputo sense.The numerical computations of convergence control parameters for the acceleration of convergence of app...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2016-01-01
|
| Series: | Journal of King Saud University: Science |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1018364715000403 |
| _version_ | 1811309318539051008 |
|---|---|
| author | V. Mishra S. Das H. Jafari S.H. Ong |
| author_facet | V. Mishra S. Das H. Jafari S.H. Ong |
| author_sort | V. Mishra |
| collection | DOAJ |
| description | In this article, Homotopy analysis method is successfully used to find the approximate solution of fractional order Van der Pol equation. The fractional derivative is described in the Caputo sense.The numerical computations of convergence control parameters for the acceleration of convergence of approximate series solution are obtained by the analysis of minimization of error for different particular cases and the results are depicted through graphs. The salient feature of the article is the graphical presentation of achieving limit cycles for different parameters. |
| first_indexed | 2024-04-13T09:40:13Z |
| format | Article |
| id | doaj.art-b9dabcb90da44bf888211ffeef3fba4e |
| institution | Directory Open Access Journal |
| issn | 1018-3647 |
| language | English |
| last_indexed | 2024-04-13T09:40:13Z |
| publishDate | 2016-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Journal of King Saud University: Science |
| spelling | doaj.art-b9dabcb90da44bf888211ffeef3fba4e2022-12-22T02:51:57ZengElsevierJournal of King Saud University: Science1018-36472016-01-01281556010.1016/j.jksus.2015.04.005Study of fractional order Van der Pol equationV. Mishra0S. Das1H. Jafari2S.H. Ong3Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi 21005, IndiaDepartment of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi 21005, IndiaDepartment of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, IranInstitute of Mathematical Sciences, University of Malaya, Kuala Lumpur 50603, MalaysiaIn this article, Homotopy analysis method is successfully used to find the approximate solution of fractional order Van der Pol equation. The fractional derivative is described in the Caputo sense.The numerical computations of convergence control parameters for the acceleration of convergence of approximate series solution are obtained by the analysis of minimization of error for different particular cases and the results are depicted through graphs. The salient feature of the article is the graphical presentation of achieving limit cycles for different parameters.http://www.sciencedirect.com/science/article/pii/S1018364715000403Oscillator equationDampingHomotopy analysis methodEmbedding parameterError analysisLimit cycle |
| spellingShingle | V. Mishra S. Das H. Jafari S.H. Ong Study of fractional order Van der Pol equation Journal of King Saud University: Science Oscillator equation Damping Homotopy analysis method Embedding parameter Error analysis Limit cycle |
| title | Study of fractional order Van der Pol equation |
| title_full | Study of fractional order Van der Pol equation |
| title_fullStr | Study of fractional order Van der Pol equation |
| title_full_unstemmed | Study of fractional order Van der Pol equation |
| title_short | Study of fractional order Van der Pol equation |
| title_sort | study of fractional order van der pol equation |
| topic | Oscillator equation Damping Homotopy analysis method Embedding parameter Error analysis Limit cycle |
| url | http://www.sciencedirect.com/science/article/pii/S1018364715000403 |
| work_keys_str_mv | AT vmishra studyoffractionalordervanderpolequation AT sdas studyoffractionalordervanderpolequation AT hjafari studyoffractionalordervanderpolequation AT shong studyoffractionalordervanderpolequation |