New Method for Solving Linear Fractional Differential Equations
We develop a new application of the Mittag-Leffler Function method that will extend the application of the method to linear differential equations with fractional order. A new solution is constructed in power series. The fractional derivatives are described in the Caputo sense. To illustrate the rel...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2011/814132 |
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| _version_ | 1832563762270306304 |
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| author | S. Z. Rida A. A. M. Arafa |
| author_facet | S. Z. Rida A. A. M. Arafa |
| author_sort | S. Z. Rida |
| collection | DOAJ |
| description | We develop a new application of the Mittag-Leffler Function method that will extend the application of the method to linear differential equations with fractional order. A new solution is constructed in power series. The fractional derivatives are described in the Caputo sense. To illustrate the reliability of the method, some examples are provided. The results reveal that the technique introduced here is very effective and convenient for solving linear differential equations of fractional order. |
| format | Article |
| id | doaj-art-36876061c5874e61aee1b102600b391b |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-36876061c5874e61aee1b102600b391b2025-02-03T01:12:31ZengWileyInternational Journal of Differential Equations1687-96431687-96512011-01-01201110.1155/2011/814132814132New Method for Solving Linear Fractional Differential EquationsS. Z. Rida0A. A. M. Arafa1Department of Mathematics, Faculty of Science, South Valley University, Qena 83523, EgyptDepartment of Mathematics, Faculty of Science, South Valley University, Qena 83523, EgyptWe develop a new application of the Mittag-Leffler Function method that will extend the application of the method to linear differential equations with fractional order. A new solution is constructed in power series. The fractional derivatives are described in the Caputo sense. To illustrate the reliability of the method, some examples are provided. The results reveal that the technique introduced here is very effective and convenient for solving linear differential equations of fractional order.http://dx.doi.org/10.1155/2011/814132 |
| spellingShingle | S. Z. Rida A. A. M. Arafa New Method for Solving Linear Fractional Differential Equations International Journal of Differential Equations |
| title | New Method for Solving Linear Fractional Differential Equations |
| title_full | New Method for Solving Linear Fractional Differential Equations |
| title_fullStr | New Method for Solving Linear Fractional Differential Equations |
| title_full_unstemmed | New Method for Solving Linear Fractional Differential Equations |
| title_short | New Method for Solving Linear Fractional Differential Equations |
| title_sort | new method for solving linear fractional differential equations |
| url | http://dx.doi.org/10.1155/2011/814132 |
| work_keys_str_mv | AT szrida newmethodforsolvinglinearfractionaldifferentialequations AT aamarafa newmethodforsolvinglinearfractionaldifferentialequations |