The Fractional Complex Step Method
It is well known that the complex step method is a tool that calculates derivatives by imposing a complex step in a strict sense. We extended the method by employing the fractional calculus differential operator in this paper. The fractional calculus can be taken in the sense of the Caputo operator,...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2013/515973 |
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| _version_ | 1832548163020390400 |
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| author | Rabha W. Ibrahim Hamid A. Jalab |
| author_facet | Rabha W. Ibrahim Hamid A. Jalab |
| author_sort | Rabha W. Ibrahim |
| collection | DOAJ |
| description | It is well known that the complex step method is a tool that calculates derivatives by imposing a complex step in a strict sense. We extended the method by employing the fractional calculus differential operator in this paper. The fractional calculus can be taken in the sense of the Caputo operator, Riemann-Liouville operator, and so forth. Furthermore, we derived several approximations for computing the fractional order derivatives. Stability of the generalized fractional complex step approximations is demonstrated for an analytic test function. |
| format | Article |
| id | doaj-art-f577c9f7b7644b84a5951fee9b8402b5 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-f577c9f7b7644b84a5951fee9b8402b52025-02-03T06:42:07ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2013-01-01201310.1155/2013/515973515973The Fractional Complex Step MethodRabha W. Ibrahim0Hamid A. Jalab1Institute of Mathematical Sciences, University of Malaya, 50603, MalaysiaFaculty of Computer Science and Information Technology, University of Malaya, 50603, MalaysiaIt is well known that the complex step method is a tool that calculates derivatives by imposing a complex step in a strict sense. We extended the method by employing the fractional calculus differential operator in this paper. The fractional calculus can be taken in the sense of the Caputo operator, Riemann-Liouville operator, and so forth. Furthermore, we derived several approximations for computing the fractional order derivatives. Stability of the generalized fractional complex step approximations is demonstrated for an analytic test function.http://dx.doi.org/10.1155/2013/515973 |
| spellingShingle | Rabha W. Ibrahim Hamid A. Jalab The Fractional Complex Step Method Discrete Dynamics in Nature and Society |
| title | The Fractional Complex Step Method |
| title_full | The Fractional Complex Step Method |
| title_fullStr | The Fractional Complex Step Method |
| title_full_unstemmed | The Fractional Complex Step Method |
| title_short | The Fractional Complex Step Method |
| title_sort | fractional complex step method |
| url | http://dx.doi.org/10.1155/2013/515973 |
| work_keys_str_mv | AT rabhawibrahim thefractionalcomplexstepmethod AT hamidajalab thefractionalcomplexstepmethod AT rabhawibrahim fractionalcomplexstepmethod AT hamidajalab fractionalcomplexstepmethod |