New solutions of fractional Drinfeld-Sokolov-Wilson system in shallow water waves

TAŞBOZAN O., Şenol M., Kurt A., Özkan O.

Ocean Engineering, vol.161, pp.62-68, 2018 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 161
  • Publication Date: 2018
  • Doi Number: 10.1016/j.oceaneng.2018.04.075
  • Journal Name: Ocean Engineering
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.62-68
  • Keywords: Conformable fractional derivative, Fractional Drinfeld-Sokolov-Wilson system, Perturbation iteration algorithm, Shallow water waves, Sine-Gordon expansion method
  • Hatay Mustafa Kemal University Affiliated: Yes

Abstract

In this paper, we present new exact solution sets of nonlinear conformable time-fractional coupled Drinfeld-Sokolov-Wilson equation which arise in shallow water flow models, when special assumptions are used to simplify the shallow water equations by means of Sine-Gordon expansion method. We also present an analytical-approximate method namely perturbation-iteration algorithm (PIA) for the system. Basic definitions of fractional derivatives are described in the conformable sense. An example is given and the results are compared to exact solutions. The results show that the presented methods are powerful, reliable, simple to use and ready to apply to wide range of fractional partial differential equations.