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On the concept of exact solution for nonlinear differential equations of fractional‐order
Author(s) -
Guner Ozkan,
Bekir Ahmet
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.3845
Subject(s) - mathematics , fractional calculus , nonlinear system , mathematical analysis , partial differential equation , transformation (genetics) , fractional programming , differential equation , space (punctuation) , biochemistry , chemistry , physics , linguistics , philosophy , quantum mechanics , gene , nonlinear programming
In this article, the new exact travelling wave solutions of the nonlinear space‐time fractional Burger's, the nonlinear space‐time fractional Telegraph and the nonlinear space‐time fractional Fisher equations have been found. Based on a nonlinear fractional complex transformation, certain fractional partial differential equations can be turned into ordinary differential equations of integer order in the sense of the Jumarie's modified Riemann–Liouville derivative. TheG ′G‐expansion method is effective for constructing solutions to the nonlinear fractional equations, and it appears to be easier and more convenient by means of a symbolic computation system. Copyright © 2016 John Wiley & Sons, Ltd.