The numerical solutions of the random time-fractional Drinfeld-Sokolov-Wilson system by the efficient method

The random time-fractional coupled Drinfeld-Sokolov-Wilson system that show up in shallow water flow models when the shallow water equations are simplified under some assumptions, is solved by q-homotopy analysis transform method (q-HATM). Caputo sense is used to define the derivatives of fractional order. The parameters and the initial conditions of this system are analyzed by Normal and Uniform distributions. The characteristics of the solutions are obtained and the 2D and 3D plots of these are simulated in Maple software. The error tables for the obtained solutions of this system are constructed. It is observed that this method is high effectiveness, too fast and extremely powerful.