This paper presents an analysis of unsteady flow of incompressible fractional
Maxwell fluid filled in the annular region between two infinite coaxial circular
cylinders. The fluid motion is created by the inner cylinder that applies a longitudinal
time-dependent shear stress and the outer cylinder that is moving at a constant velocity.
The velocity field and shear stress are determined using the Laplace and finite
Hankel transforms. Obtained solutions are presented in terms of the generalized G and
R functions. We also obtain the solutions for ordinary Maxwell fluid and Newtonian
fluid as special cases of generalized solutions. The influence of different parameters
on the velocity field and shear stress are also presented using graphical illustration.
Finally, a comparison is drawn between motions of fractional Maxwell fluid, ordinary
Maxwell fluid and Newtonian fluid.