A numerical study of the Van der Pol model derived by the Caputo–Fabrizio operator
The study of nonlinear oscillators is an important topic in the development of the theory of dynamical systems. In this research, a nonlinear fractional model is introduced, which is called the fractional Van der Pol model. This modified model is derived using the Caputo–Fabrizio operator. Achieving...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
AIP Publishing LLC
2023-08-01
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| Series: | AIP Advances |
| Online Access: | http://dx.doi.org/10.1063/5.0167878 |
| _version_ | 1827821766992461824 |
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| author | H. Jafari R. M. Ganji N. Ramroodi S. Salati D. D. Ganji |
| author_facet | H. Jafari R. M. Ganji N. Ramroodi S. Salati D. D. Ganji |
| author_sort | H. Jafari |
| collection | DOAJ |
| description | The study of nonlinear oscillators is an important topic in the development of the theory of dynamical systems. In this research, a nonlinear fractional model is introduced, which is called the fractional Van der Pol model. This modified model is derived using the Caputo–Fabrizio operator. Achieving the solution of this model is not easy. Therefore, in this research, an efficient algorithm for solving this fractional model is evaluated. This algorithm is supported by the three-step Adams–Bashforth process. A significant feature of this research is the graphical presentation of achieving limit cycles for various parameters. |
| first_indexed | 2024-03-12T01:48:42Z |
| format | Article |
| id | doaj.art-cc0aa6633f904b6180929d6aab18fa2c |
| institution | Directory Open Access Journal |
| issn | 2158-3226 |
| language | English |
| last_indexed | 2024-03-12T01:48:42Z |
| publishDate | 2023-08-01 |
| publisher | AIP Publishing LLC |
| record_format | Article |
| series | AIP Advances |
| spelling | doaj.art-cc0aa6633f904b6180929d6aab18fa2c2023-09-08T16:03:30ZengAIP Publishing LLCAIP Advances2158-32262023-08-01138085127085127-1010.1063/5.0167878A numerical study of the Van der Pol model derived by the Caputo–Fabrizio operatorH. Jafari0R. M. Ganji1N. Ramroodi2S. Salati3D. D. Ganji4Department of Applied Mathematics, University of Mazandaran, Babolsar, IranDepartment of Applied Mathematics, University of Mazandaran, Babolsar, IranFaculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, IranDepartment of Applied Mathematics, University of Mazandaran, Babolsar, IranDepartment of Mechanical Engineering, Babol University of Technology, Babol, IranThe study of nonlinear oscillators is an important topic in the development of the theory of dynamical systems. In this research, a nonlinear fractional model is introduced, which is called the fractional Van der Pol model. This modified model is derived using the Caputo–Fabrizio operator. Achieving the solution of this model is not easy. Therefore, in this research, an efficient algorithm for solving this fractional model is evaluated. This algorithm is supported by the three-step Adams–Bashforth process. A significant feature of this research is the graphical presentation of achieving limit cycles for various parameters.http://dx.doi.org/10.1063/5.0167878 |
| spellingShingle | H. Jafari R. M. Ganji N. Ramroodi S. Salati D. D. Ganji A numerical study of the Van der Pol model derived by the Caputo–Fabrizio operator AIP Advances |
| title | A numerical study of the Van der Pol model derived by the Caputo–Fabrizio operator |
| title_full | A numerical study of the Van der Pol model derived by the Caputo–Fabrizio operator |
| title_fullStr | A numerical study of the Van der Pol model derived by the Caputo–Fabrizio operator |
| title_full_unstemmed | A numerical study of the Van der Pol model derived by the Caputo–Fabrizio operator |
| title_short | A numerical study of the Van der Pol model derived by the Caputo–Fabrizio operator |
| title_sort | numerical study of the van der pol model derived by the caputo fabrizio operator |
| url | http://dx.doi.org/10.1063/5.0167878 |
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