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

• Published in: Ocean engineering 2018-08, Vol.161, p.62-68
• Main Authors: Tasbozan, Orkun, Şenol, Mehmet, Kurt, Ali, Özkan, Ozan
• Format: Article
• Language: English
• Subjects: Conformable fractional derivative; Fractional Drinfeld-Sokolov-Wilson system; Perturbation iteration algorithm; Shallow water waves; Sine-Gordon expansion method
• ISSN: 0029-8018; 1873-5258
• DOI: 10.1016/j.oceaneng.2018.04.075

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. •In this case study, firstly sine-Gordon expansion method is implemented to obtain exact solution sets of time-fractional coupled Drinfeld-Sokolov-Wilson system of equations comes with shallow water waves.•Also perturbation-iteration algorithm (PIA) is used to obtained some approximate solutions of the system.•It is observed that the sine-Gordon expansion method is reliable and effective tool for handling FPDEs.•Also the numerical results obtained by PIA are compared with the exact solutions for α=0.25,α=0.5,α=0.75.•They reveal the fast convergence rate of the PIA even after computing a few iterations.•The method does not require any assumptions, transformations or discretizations.•It is therefore clear that the both methods are reliable, powerful and easy to implement.•The results prove that the present methods could be applied to various fractional linear and nonlinear models occurring in different branches of science and engineering.