In this paper, by introducing the fractional derivative in sense of Caputo, the Laplace- variational iteration
method (LVIM) and the Laplace-Adomian decomposition method (LADM) are directly extended to study
the linear and nonlinear systems of fractional partial differential equations, as a result the approximated
numerical solutions are acquired in the form of rapidly convergent series with easily computable components. Numerical results show that the two approaches are easy to implement and accurate when are
applied. Compassions are made between the two methods and exact solutions. Figures are used to show
the efficiency as well as the accuracy of the achieved approximated results.