Numerical approaches to system of fractional partial differential equations
In this paper, by introducing the fractional derivative in sense of Caputo, the Laplace- variational iteration method (LVIM) and the Laplace-Adomian decomposition method (LADM) are directly extended to study the linear and nonlinear systems of fractional partial differential equations, as a result t...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-04-01
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| Series: | Journal of the Egyptian Mathematical Society |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110256X16300773 |
| _version_ | 1811235643630551040 |
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| author | H. F. Ahmed Mohamed S. M. Bahgat Mofida Zaki |
| author_facet | H. F. Ahmed Mohamed S. M. Bahgat Mofida Zaki |
| author_sort | H. F. Ahmed |
| collection | DOAJ |
| description | In this paper, by introducing the fractional derivative in sense of Caputo, the Laplace- variational iteration method (LVIM) and the Laplace-Adomian decomposition method (LADM) are directly extended to study the linear and nonlinear systems of fractional partial differential equations, as a result the approximated numerical solutions are acquired in the form of rapidly convergent series with easily computable components. Numerical results show that the two approaches are easy to implement and accurate when are applied. Compassions are made between the two methods and exact solutions. Figures are used to show the efficiency as well as the accuracy of the achieved approximated results. |
| first_indexed | 2024-04-12T11:54:21Z |
| format | Article |
| id | doaj.art-fc0425a1f9ee4b1880c2cc1d7c09cac7 |
| institution | Directory Open Access Journal |
| issn | 1110-256X |
| language | English |
| last_indexed | 2024-04-12T11:54:21Z |
| publishDate | 2017-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of the Egyptian Mathematical Society |
| spelling | doaj.art-fc0425a1f9ee4b1880c2cc1d7c09cac72022-12-22T03:34:03ZengSpringerOpenJournal of the Egyptian Mathematical Society1110-256X2017-04-0125214115010.1016/j.joems.2016.12.004Numerical approaches to system of fractional partial differential equationsH. F. AhmedMohamed S. M. BahgatMofida ZakiIn this paper, by introducing the fractional derivative in sense of Caputo, the Laplace- variational iteration method (LVIM) and the Laplace-Adomian decomposition method (LADM) are directly extended to study the linear and nonlinear systems of fractional partial differential equations, as a result the approximated numerical solutions are acquired in the form of rapidly convergent series with easily computable components. Numerical results show that the two approaches are easy to implement and accurate when are applied. Compassions are made between the two methods and exact solutions. Figures are used to show the efficiency as well as the accuracy of the achieved approximated results.http://www.sciencedirect.com/science/article/pii/S1110256X16300773Adomian decomposition methodVariational iteration methodLagrange multiplierCaputo fractional derivative |
| spellingShingle | H. F. Ahmed Mohamed S. M. Bahgat Mofida Zaki Numerical approaches to system of fractional partial differential equations Journal of the Egyptian Mathematical Society Adomian decomposition method Variational iteration method Lagrange multiplier Caputo fractional derivative |
| title | Numerical approaches to system of fractional partial differential equations |
| title_full | Numerical approaches to system of fractional partial differential equations |
| title_fullStr | Numerical approaches to system of fractional partial differential equations |
| title_full_unstemmed | Numerical approaches to system of fractional partial differential equations |
| title_short | Numerical approaches to system of fractional partial differential equations |
| title_sort | numerical approaches to system of fractional partial differential equations |
| topic | Adomian decomposition method Variational iteration method Lagrange multiplier Caputo fractional derivative |
| url | http://www.sciencedirect.com/science/article/pii/S1110256X16300773 |
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