The fractional natural decomposition method: theories and applications

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
1. Verfasser: Rawashdeh, Mahmoud S.
Format: Artikel
Sprache:eng
Schlagworte:
Adomian decomposition method
Caputo derivative
Decomposition
Derivatives
fractional derivative
Mathematical analysis
Mathematical models
natural transform
Nonlinearity
Theorem proving
Theorems
Transforms
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Zusammenfassung: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.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.4144