This manuscript employs the Shehu Transform in combination with the Adomian Decomposition Method (ADM), the Modified Adomian Decomposition Method (MADM), and the New Iteration Method (NIM) to obtain a series solution for the time-fractional Drinfeld-Sokolov-Wilson (DSW) equations. These equations model gravitational water flows affected by shear stress, covering situations like flows through vegetation, overland flows, dam breaks, and floods. To verify the accuracy of the solutions derived using the Shehu Transform Adomian Decomposition Method (STADM) and the Shehu Transform Modified Adomian Decomposition Method (STMADM), the relative absolute error for the series solutions is calculated for α=1, where α represents the fractional time derivative and lies within the range α<1. The Shehu transform Modified Adomian Decomposition Method (STMADM) generally provides a better approximation with a smaller error than the standard STADM. Finally, the results obtained by the Homotopy Perturbation Method (HPM) and the New Iteration Method (NIM) are fairly comparable to the solutions provided by the STMADM. This suggests that the outcomes generated by STMADM and the Shehu Transform New Iteration Method (STNIM) are very similar. Using both STMADM and STNIM to time-fractional differential equations yields comparable and reliable results, it can be inferred.