(4)New analytic solutions of the space-time fractional Broer–Kaup and approximate long water wave equations

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H. Çerdik Yaslan

Department of Mathematics, Pamukkale University, Denizli 20070, Turkey 

Received 29 April 2018; received in revised form 20 October 2018; accepted 20 October 2018 

Available online 26 October 2018 

Abstract

    In the present paper, the exp (−φ(ξ )) expansion method is applied to the fractional Broer–Kaup and approximate long water wave equations. The explicit approximate traveling wave solutions are obtained by using this method. Here, fractional derivatives are defined in the conformable sense. The obtained traveling wave solutions are expressed by the hyperbolic, trigonometric, exponential and rational functions. Simulations of the obtained solutions are given at the end of the paper. 

© 2018 Shanghai Jiaotong University. Published by Elsevier B.V. 

This is an open access article under the CC BY-NC-ND license. (http://creativecommons.org/licenses/by-nc-nd/4.0/)  

Keywords: The fractional Broer–Kaup equations; The fractional approximate long water wave equations; Conformable derivative; 

exp (−φ(ξ )) expansion method; Traveling wave solutions.