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.

在本文中，我们首次对 Drinfeld-Sokolov-Wilson 方程 (DSWE) 和耦合粘性 Burgers 方程 (CVBE) 的时间分数系统实施一致拉普拉斯分解方法 (CLDM)。DSWE和CVBE在近海、近海研究中占有重要地位，分别被认为是浅水波浪和流体动力学湍流的数学模型。最后，借助表格和图形将得到的解与精确解进行比较。所得结果表明，一致拉普拉斯分解法(CLDM)高效、可靠、易于应用，为研究人员求解物理学中的各种非线性分数阶偏微分方程提供了新的视角。