Journal of Ocean Engineering and Science

Volume 4, Issue 1

(1)Boussinesq equations: M-fractional solitary wave solutions and convergence analysis

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Tukur Abdulkadir Sulaiman ^a,b,∗, Hasan Bulut ^a,c

^aFaculty of Science, Firat University, Elazig, Turkey

^bFaculty of Science, Federal University Dutse, Jigawa, Nigeria

^cFaculty of Education, Final International University, Kyrenia, Cyprus

Received 29 November 2018; received in revised form 8 December 2018; accepted 9 December 2018

Available online 11 December 2018

Abstract

The studies of the dynamics behaviors of nonlinear models arising in ocean engineering play a signiﬁcant role in our daily activities. This study investigates the nonlinear fractional modiﬁed Boussinesq equation and the fractional bad Boussinesq equation using the extended sinh- Gordon equation expansion method. Several travelling wave solutions are successfully constructed. By choosing suitable values of parameters, the 2D and 3D graphs of the reported solutions are successfully plotted. The convergence analysis of the applied method is also discussed. © 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 Sinh-Gordon equation; Boussinesq equations; Solitons; M-fractional derivative; Convergence analysis.