Analytical Solutions of Fractional Klein-Gordon and Gas Dynamics Equations, via the (G′/G)-Expansion Method
Department of Mathematics, Abdul Wali khan University, Mardan 23200, Pakistan
Department of Mathematics, Allama Iqbal Open University, Islamabad 44000, Pakistan
Theoretical and Computational Science (TaCS) Center Department of Mathematics, Faculty of Science, King Mongkuts University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, Thailand
Department of Medical Research, China Medical University, Taichung 40402, Taiwan
Author to whom correspondence should be addressed.
Received: 2 April 2019 / Revised: 12 April 2019 / Accepted: 14 April 2019 / Published: 19 April 2019
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In this article, the
-expansion method is used for the analytical solutions of fractional-order Klein-Gordon and Gas Dynamics equations. The fractional derivatives are defined in the term of Jumarie’s operator. The proposed method is based on certain variable transformation, which transforms the given problems into ordinary differential equations. The solution of resultant ordinary differential equation can be expressed by a polynomial in
satisfies a second order linear ordinary differential equation. In this paper,
-expansion method will represent, the travelling wave solutions of fractional-order Klein-Gordon and Gas Dynamics equations in the term of trigonometric, hyperbolic and rational functions.
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Khan, H.; Barak, S.; Kumam, P.; Arif, M. Analytical Solutions of Fractional Klein-Gordon and Gas Dynamics Equations, via the (G′/G)-Expansion Method. Symmetry 2019, 11, 566.
Khan H, Barak S, Kumam P, Arif M. Analytical Solutions of Fractional Klein-Gordon and Gas Dynamics Equations, via the (G′/G)-Expansion Method. Symmetry. 2019; 11(4):566.
Khan, Hassan; Barak, Shoaib; Kumam, Poom; Arif, Muhammad. 2019. "Analytical Solutions of Fractional Klein-Gordon and Gas Dynamics Equations, via the (G′/G)-Expansion Method." Symmetry 11, no. 4: 566.
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