Two Reliable Methods for Solving the (3 + 1)-Dimensional Space-Time Fractional Jimbo-Miwa Equation

We investigate methods for obtaining exact solutions of the (3 + 1)-dimensional nonlinear space-time fractional Jimbo-Miwa equation in the sense of the modified Riemann-Liouville derivative. The methods employed to analytically solve the equation are the G′/G,1/G-expansion method and the novel G′/G-...

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Bibliographic Details
Published in:Mathematical problems in engineering 2017-01, Vol.2017 (2017), p.1-30
Main Authors: Porka, Wanassanun, Khaopant, Chaowanee, Koonprasert, Sanoe, Sirisubtawee, Sekson
Format: Article
Language:English
Subjects:
Applied mathematics
Evolution
Exact solutions
Finite volume method
Fractals
Mathematical analysis
Mathematical problems
Partial differential equations
Physics
Rational functions
Software packages
Spacetime
Trustworthiness
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Summary:We investigate methods for obtaining exact solutions of the (3 + 1)-dimensional nonlinear space-time fractional Jimbo-Miwa equation in the sense of the modified Riemann-Liouville derivative. The methods employed to analytically solve the equation are the G′/G,1/G-expansion method and the novel G′/G-expansion method. To the best of our knowledge, there are no researchers who have applied these methods to obtain exact solutions of the equation. The application of the methods is simple, elegant, efficient, and trustworthy. In particular, applying the novel G′/G-expansion method to the equation, we obtain more exact solutions than using other existing methods such as the G′/G-expansion method and the exp-Φ(ξ)-expansion method. The exact solutions of the equation, obtained using the two methods, can be categorized in terms of hyperbolic, trigonometric, and rational functions. Some of the results obtained by the two methods are new and reported here for the first time. In addition, the obtained exact explicit solutions of the equation characterize many physical meanings such as soliton solitary wave solutions, periodic wave solutions, and singular multiple-soliton solutions.
ISSN:1024-123X
1563-5147
DOI:10.1155/2017/9257019