An extension of the so-called newiterativemethod (NIM) has been used to handle linear and nonlinear fractional partial differential
equations.Themain property of themethod lies in its flexibility and ability to solve nonlinear equations accurately and conveniently.
Therefore, a general framework of the NIM is presented for analytical treatment of fractional partial differential equations in fluid
mechanics. The fractional derivatives are described in the Caputo sense. Numerical illustrations that include the fractional wave
equation, fractional Burgers equation, fractional KdV equation, fractional Klein-Gordon equation, and fractional Boussinesq-like
equation are investigated to show the pertinent features of the technique. Comparison of the results obtained by the NIM with
those obtained by both Adomian decomposition method (ADM) and the variational iteration method (VIM) reveals that the NIM
is very effective and convenient. The basic idea described in this paper is expected to be further employed to solve other similar
linear and nonlinear problems in fractional calculus.