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In this paper, the generalized differential transform method is implemented for solving several linear fractional partial differential equations arising in fluid mechanics. This method is based on the two-dimensional differential transform method (DTM) and generalized Taylor's formula. Numerical illustrations of the time-fractional diffusion equation and the time-fractional wave equation are investigated to demonstrate the effectiveness of this method. Results obtained by using the scheme presented here agree well with the analytical solutions and the numerical results presented elsewhere. The results reveal the method is feasible and convenient for handling approximate solutions of linear or nonlinear fractional partial differential equations.