Journal of Ocean Engineering and Science

Volume 6, Issue 3

(2)SITEM for the conformable space-time fractional Boussinesq and (2 + 1)-dimensional breaking soliton equations

H. Çerdik Yaslan^∗ , Ayse Girgin

Department of Mathematics, Pamukkale University, Denizli 20070, Turkey

Received 24 October 2019; received in revised form 16 December 2019; accepted 23 November 2020

Available online 11 December 2020

Abstract

In the present paper, new analytical solutions for the space-time fractional Boussinesq and (2 + 1)-dimensional breaking soliton equations are obtained by using the simplified tan( φ(ξ) 2 )-expansion method. Here, fractional derivatives are defined in the conformable sense. To show the correctness of the obtained traveling wave solutions, residual error function is defined. It is observed that the new solutions are very close to the exact solutions. The solutions obtained by the presented method have not been reported in former literature.

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

Keywords: Space-time fractional Boussinesq equation; (2 + 1)-dimensional breaking soliton equation; Simplified tan( φ(ξ) 2 )-expansion method (SITEM); Conformable derivative.