The fractional natural decomposition method: theories and applications
In this paper, we propose a new method called the fractional natural decomposition method (FNDM). We give the proof of new theorems of the FNDM, and we extend the natural transform method to fractional derivatives. We apply the FNDM to construct analytical and approximate solutions of the nonlinear...
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| Veröffentlicht in: | Mathematical methods in the applied sciences 2017-05, Vol.40 (7), p.2362-2376 |
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| container_title | Mathematical methods in the applied sciences |
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| creator | Rawashdeh, Mahmoud S. |
| description | In this paper, we propose a new method called the fractional natural decomposition method (FNDM). We give the proof of new theorems of the FNDM, and we extend the natural transform method to fractional derivatives. We apply the FNDM to construct analytical and approximate solutions of the nonlinear time‐fractional Harry Dym equation and the nonlinear time‐fractional Fisher's equation. The fractional derivatives are described in the Caputo sense. The effectiveness of the FNDM is numerically confirmed. Copyright © 2016 John Wiley & Sons, Ltd. |
| doi_str_mv | 10.1002/mma.4144 |
| format | Article |
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| source | Wiley Online Library Journals Frontfile Complete |
| subjects | Adomian decomposition method Caputo derivative Decomposition Derivatives fractional derivative Mathematical analysis Mathematical models natural transform Nonlinearity Theorem proving Theorems Transforms |
| title | The fractional natural decomposition method: theories and applications |
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