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In the concerned article, we present the numerical solution of nonlinear coupled system of Whitham-Broer-Kaup equations (WBK) of fractional order. With the help of Laplace transform coupled with Adomian decomposition method, an iterative procedure is established to investigate approximate solution to the proposed coupled system of nonlinear partial fractional differential equations. The concerned techniques are demonstrated by some numerical examples. Also, we compared the results of our proposed method with the results of other well known numerical methods such as Variation iteration method (VIM), Adomian decomposition method (ADM) and Homotopy perturbation method (HPM). For computation, we use Maple 18 and Matlab. Keywords: Whitham-Broer-Kaup equations, Non-linear partial fractional differential equation, Laplace-Adomian decomposition method, Numerical solutions