In this paper, it is the first time that we implement conformable Laplace decomposition method (CLDM) to time fractional systems of Drinfeld-Sokolov-Wilson equation (DSWE) and coupled viscous Burgers’ equation (CVBE). DSWE and CVBE have an important place for cceanic, coastal sea research and they are considered as a mathematical model for shallow water waves and hydrodynmic turbulence respectively. At the end, the obtained solutions are compared with the exact solutions by the aid of tables and figures. The obtained results show that,conformable Laplace decomposition method (CLDM) is efficient, reliable, easy to apply and it gives researchers a new perspective for solving a wide variety of nonlinear fractional partial differential equations in physics.