A robust semi-analytical approach to study fractional coupled Sokolov Wilson system in shallow water waves

In this paper, a semi-analytical approach namely, modified differential transform method is suggested to investigate coupled fractional nonlinear Drinfeld-Sokolov-Wilson equations (CFDSWE) that arise in shallow water flow models. The Caputo sense is used to characterise the fractional derivative. The solution of coupled fractional nonlinear Drinfeld-Sokolov-Wilson equations is obtained for two different cases. The obtained solution shows an excellent agreement with the exact solution for classical order which shows the effectiveness and reliability of the method. The results show that the fractional modified differential transform method is a promising tool to find the analytical solution of highly nonlinear fractional PDEs. The computational work is done in the MATLAB software package.