Pade Method for Construction of Numerical Algorithms for Fractional Initial Value Problem
In this paper, we propose an efficient method for constructing numerical algorithms for solving the fractional initial value problem by using the Pade approximation of fractional derivative operators. We regard the Grunwald–Letnikov fractional derivative as a kind of Taylor series and get the approx...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2020/8964759 |
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| _version_ | 1832556895995428864 |
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| author | Feng Gao Chunmei Chi |
| author_facet | Feng Gao Chunmei Chi |
| author_sort | Feng Gao |
| collection | DOAJ |
| description | In this paper, we propose an efficient method for constructing numerical algorithms for solving the fractional initial value problem by using the Pade approximation of fractional derivative operators. We regard the Grunwald–Letnikov fractional derivative as a kind of Taylor series and get the approximation equation of the Taylor series by Pade approximation. Based on the approximation equation, we construct the corresponding numerical algorithms for the fractional initial value problem. Finally, we use some examples to illustrate the applicability and efficiency of the proposed technique. |
| format | Article |
| id | doaj-art-710809c848b2408e9a7a5957ef1e632d |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-710809c848b2408e9a7a5957ef1e632d2025-02-03T05:44:13ZengWileyJournal of Mathematics2314-46292314-47852020-01-01202010.1155/2020/89647598964759Pade Method for Construction of Numerical Algorithms for Fractional Initial Value ProblemFeng Gao0Chunmei Chi1School of Science, Qingdao University of Technology, Qingdao 266033, ChinaSchool of Science, Qingdao University of Technology, Qingdao 266033, ChinaIn this paper, we propose an efficient method for constructing numerical algorithms for solving the fractional initial value problem by using the Pade approximation of fractional derivative operators. We regard the Grunwald–Letnikov fractional derivative as a kind of Taylor series and get the approximation equation of the Taylor series by Pade approximation. Based on the approximation equation, we construct the corresponding numerical algorithms for the fractional initial value problem. Finally, we use some examples to illustrate the applicability and efficiency of the proposed technique.http://dx.doi.org/10.1155/2020/8964759 |
| spellingShingle | Feng Gao Chunmei Chi Pade Method for Construction of Numerical Algorithms for Fractional Initial Value Problem Journal of Mathematics |
| title | Pade Method for Construction of Numerical Algorithms for Fractional Initial Value Problem |
| title_full | Pade Method for Construction of Numerical Algorithms for Fractional Initial Value Problem |
| title_fullStr | Pade Method for Construction of Numerical Algorithms for Fractional Initial Value Problem |
| title_full_unstemmed | Pade Method for Construction of Numerical Algorithms for Fractional Initial Value Problem |
| title_short | Pade Method for Construction of Numerical Algorithms for Fractional Initial Value Problem |
| title_sort | pade method for construction of numerical algorithms for fractional initial value problem |
| url | http://dx.doi.org/10.1155/2020/8964759 |
| work_keys_str_mv | AT fenggao pademethodforconstructionofnumericalalgorithmsforfractionalinitialvalueproblem AT chunmeichi pademethodforconstructionofnumericalalgorithmsforfractionalinitialvalueproblem |