An optimal method for approximating the delay differential equations of noninteger order
Abstract The main purpose of this paper is to use a method with a free parameter, named the optimal asymptotic homotopy method (OHAM), in order to obtain the solution of delay differential equations, delay partial differential equations, and a system of coupled delay equations featuring fractional d...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-08-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-018-1717-5 |
| _version_ | 1818035045476073472 |
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| author | Dumitru Baleanu Bahram Agheli Rahmat Darzi |
| author_facet | Dumitru Baleanu Bahram Agheli Rahmat Darzi |
| author_sort | Dumitru Baleanu |
| collection | DOAJ |
| description | Abstract The main purpose of this paper is to use a method with a free parameter, named the optimal asymptotic homotopy method (OHAM), in order to obtain the solution of delay differential equations, delay partial differential equations, and a system of coupled delay equations featuring fractional derivative. This method is preferable to others since it has faster convergence toward homotopy perturbation method, and the convergence rate can be set as a controlled area. Various examples are given to better understand the use of this method. The approximate solutions are compared with exact solutions as well. |
| first_indexed | 2024-12-10T06:48:49Z |
| format | Article |
| id | doaj.art-71d9b5dfa7d147408adda49b4f5d5395 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-10T06:48:49Z |
| publishDate | 2018-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-71d9b5dfa7d147408adda49b4f5d53952022-12-22T01:58:36ZengSpringerOpenAdvances in Difference Equations1687-18472018-08-012018111510.1186/s13662-018-1717-5An optimal method for approximating the delay differential equations of noninteger orderDumitru Baleanu0Bahram Agheli1Rahmat Darzi2Department of Mathematics, Çankaya UniversityDepartment of Mathematics, Qaemshahr Branch, Islamic Azad UniversityDepartment of Mathematics, Neka Branch, Islamic Azad UniversityAbstract The main purpose of this paper is to use a method with a free parameter, named the optimal asymptotic homotopy method (OHAM), in order to obtain the solution of delay differential equations, delay partial differential equations, and a system of coupled delay equations featuring fractional derivative. This method is preferable to others since it has faster convergence toward homotopy perturbation method, and the convergence rate can be set as a controlled area. Various examples are given to better understand the use of this method. The approximate solutions are compared with exact solutions as well.http://link.springer.com/article/10.1186/s13662-018-1717-5Delay differential equationsOptimal homotopy asymptoticCaputo derivative |
| spellingShingle | Dumitru Baleanu Bahram Agheli Rahmat Darzi An optimal method for approximating the delay differential equations of noninteger order Advances in Difference Equations Delay differential equations Optimal homotopy asymptotic Caputo derivative |
| title | An optimal method for approximating the delay differential equations of noninteger order |
| title_full | An optimal method for approximating the delay differential equations of noninteger order |
| title_fullStr | An optimal method for approximating the delay differential equations of noninteger order |
| title_full_unstemmed | An optimal method for approximating the delay differential equations of noninteger order |
| title_short | An optimal method for approximating the delay differential equations of noninteger order |
| title_sort | optimal method for approximating the delay differential equations of noninteger order |
| topic | Delay differential equations Optimal homotopy asymptotic Caputo derivative |
| url | http://link.springer.com/article/10.1186/s13662-018-1717-5 |
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