This paper introduces a new modification of least squares homotopy perturbation method (LSHPM) for solving linear and nonlinear fractional partial differential equations (FPDEs). The main advantage of the new modification is to approximate the solution for FPDEs in a full general set. Moreover, the convergence of the proposed modification is shown. Analytical and numerical solutions for the linear Navier-Stokes equation and the nonlinear gas dynamic equation are successfully obtained to confirm the accuracy and efficiency of the proposed modification.