In this article, two powerful techniques called variational iteration and
Adomian decomposition methods are proposed to solve analytically the
fractional form of the fourth order nonlinear ordinary differential
equation which reduced by similarity transformation from the basic
system of nonlinear partial differential equations of motion of an
unsteady axisymmetric flow of nonconducting, Newtonian fluid
squeezed between two circular plates with slip and no-slip boundaries.
The analysis of convergence of the proposed methods is discussed
through the absolute residual errors for various Reynolds number and
various values of the fractional order. Comparisons between the results
obtained by the proposed methods with those obtained by the new
iterative and Picard methods are made which confirm that the proposed
methods are powerful methods and therefore suitable for solving this
kind of problems.