A Numerical Method for Delayed Fractional-Order Differential Equations
A numerical method for nonlinear fractional-order differential equations with constant or time-varying delay is devised. The order here is an arbitrary positive real number, and the differential operator is with the Caputo definition. The general Adams-Bashforth-Moulton method combined with the line...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/256071 |
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| _version_ | 1832562523971256320 |
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| author | Zhen Wang |
| author_facet | Zhen Wang |
| author_sort | Zhen Wang |
| collection | DOAJ |
| description | A numerical method for nonlinear fractional-order differential equations with constant or time-varying delay is devised. The order here is an arbitrary positive real number, and the differential operator is with the Caputo definition. The general Adams-Bashforth-Moulton method combined with the linear interpolation method is employed to approximate the delayed fractional-order differential equations. Meanwhile, the detailed error analysis for this algorithm is given. In order to compare with the exact analytical solution, a numerical example is provided to illustrate the effectiveness of the proposed method. |
| format | Article |
| id | doaj-art-3a3159faccab42d2a87cd440b9c5b15f |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-3a3159faccab42d2a87cd440b9c5b15f2025-02-03T01:22:28ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/256071256071A Numerical Method for Delayed Fractional-Order Differential EquationsZhen Wang0College of Information Science and Engineering, Shandong University of Science and Technology, Qingdao 266590, ChinaA numerical method for nonlinear fractional-order differential equations with constant or time-varying delay is devised. The order here is an arbitrary positive real number, and the differential operator is with the Caputo definition. The general Adams-Bashforth-Moulton method combined with the linear interpolation method is employed to approximate the delayed fractional-order differential equations. Meanwhile, the detailed error analysis for this algorithm is given. In order to compare with the exact analytical solution, a numerical example is provided to illustrate the effectiveness of the proposed method.http://dx.doi.org/10.1155/2013/256071 |
| spellingShingle | Zhen Wang A Numerical Method for Delayed Fractional-Order Differential Equations Journal of Applied Mathematics |
| title | A Numerical Method for Delayed Fractional-Order Differential Equations |
| title_full | A Numerical Method for Delayed Fractional-Order Differential Equations |
| title_fullStr | A Numerical Method for Delayed Fractional-Order Differential Equations |
| title_full_unstemmed | A Numerical Method for Delayed Fractional-Order Differential Equations |
| title_short | A Numerical Method for Delayed Fractional-Order Differential Equations |
| title_sort | numerical method for delayed fractional order differential equations |
| url | http://dx.doi.org/10.1155/2013/256071 |
| work_keys_str_mv | AT zhenwang anumericalmethodfordelayedfractionalorderdifferentialequations AT zhenwang numericalmethodfordelayedfractionalorderdifferentialequations |