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In this paper, a numerical method for fourth-order  time-fractional partial differential equations with variable coefficients is proposed. Our method consists of  Laplace transform,  the homotopy perturbation method and  Stehfest's numerical inversion algorithm. We show the validity and efficiency of the proposed method (so called LHPM) by applying it to some examples and comparing the results obtained by this method with the ones found by Adomian decomposition method (ADM)  and He's variational iteration method (HVIM).

NUMERICAL SOLUTION OF FOURTH-ORDER TIME-FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS WITH VARIABLE COEFFICIENTS