New Iterative Method for Solving a Coupled System of Fractional-Order Drinfeld-Sokolov-Wilson (FDSW) and Fractional Shallow Water (FSW) Equations

In this study, the new iterative method has been applied to a coupled system of fractional-order Drinfeld-Sokolov-Wilson (FDSW) and fractional shallow water (FSW) equations. The fractional-order derivatives are taken in the Caputo sense whose order is between 0 and 1. The suggested method is capable to handle the FDEs without any transformation and discretization. The obtained results have been compared with the exact solution and with the q-homotopy analysis transform method. The outcomes show the efficiency and effectiveness of NIM by comparing through tables and graphs.