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Research Articles

Closed form wave solutions to the time fractional Boussinesq-type equation and the Zakharov-Kuznetsov equation

Authors:

M Nurul Islam,

Department of Mathematics, Islamic University-Kushtia, Bangladesh, BD
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Md Ashrafuzzaman Khan,

Department of Applied Mathematics, University of Rajshahi, Bangladesh, BD
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M Ali Akbar

Department of Applied Mathematics, University of Rajshahi, Bangladesh, BD
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Abstract

In this article, we have considered the time fractional Boussinesq-type equation and the (3, 3,.3) time fractional Zakharov-Kuznetsov (FZK) equation, as the model of fluid flow and heat transfer, temperature changes from one place to another, waves on a free-moving fluid surface, periodic and shallow water waves, conservation of mass, ion-acoustic waves in plasma, electromagnetic waves, traffic flow and signal processing waves of optical fibers, etc. Applying the generalised (G'/G)-expansion method and by means of fractional complex transformation, we have examined fresh, useful and further generalised exact travelling wave solutions to the above mentioned equations. We have shown that the method used in this article is a more generalised, straightforward and efficient technique that can be used to establish a large number of fresh solutions of the fractional nonlinear differential equations involved in mathematical physics. We have also discussed the physical explanation for its definite values of emerging parameters of the solutions, which are examined from these equations.  Finally we have depicted the 3D and 2D figures to the sense of physical phenomena of the obtained solutions.

How to Cite: Islam, M.N., Khan, M.A. and Akbar, M.A., 2019. Closed form wave solutions to the time fractional Boussinesq-type equation and the Zakharov-Kuznetsov equation. Journal of the National Science Foundation of Sri Lanka, 47(2).
Published on 21 May 2019.
Peer Reviewed

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