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The fractional natural decomposition method: theories and applications
Author(s) -
Rawashdeh Mahmoud S.
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4144
Subject(s) - mathematics , fractional calculus , nonlinear system , decomposition method (queueing theory) , decomposition , construct (python library) , calculus (dental) , mathematical analysis , discrete mathematics , computer science , medicine , ecology , physics , dentistry , quantum mechanics , biology , programming language
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.