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Chin. Phys. B, 2016, Vol. 25(4): 040204    DOI: 10.1088/1674-1056/25/4/040204
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New analytical exact solutions of time fractional KdV–KZK equation by Kudryashov methods

S Saha Ray
National Institute of Technology, Department of Mathematics, Rourkela-769008, India
Abstract  In this paper, new exact solutions of the time fractional KdV-Khokhlov-Zabolotskaya-Kuznetsov (KdV-KZK) equation are obtained by the classical Kudryashov method and modified Kudryashov method respectively. For this purpose, the modified Riemann-Liouville derivative is used to convert the nonlinear time fractional KdV-KZK equation into the nonlinear ordinary differential equation. In the present analysis, the classical Kudryashov method and modified Kudryashov method are both used successively to compute the analytical solutions of the time fractional KdV-KZK equation. As a result, new exact solutions involving the symmetrical Fibonacci function, hyperbolic function and exponential function are obtained for the first time. The methods under consideration are reliable and efficient, and can be used as an alternative to establish new exact solutions of different types of fractional differential equations arising from mathematical physics. The obtained results are exhibited graphically in order to demonstrate the efficiencies and applicabilities of these proposed methods of solving the nonlinear time fractional KdV-KZK equation.
Keywords:  KdV-Khokhlov-Zabolotskaya-Kuznetsov equation      Kudryashov method      modified Kudryashov method      fractional complex transform      modified Riemann-Liouville derivative  
Received:  30 August 2015      Revised:  23 November 2015      Accepted manuscript online: 
PACS:  02.70.-c (Computational techniques; simulations)  
Corresponding Authors:  S Saha Ray     E-mail:  santanusaharay@yahoo.com

Cite this article: 

S Saha Ray New analytical exact solutions of time fractional KdV–KZK equation by Kudryashov methods 2016 Chin. Phys. B 25 040204

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