Exact solutions for the unsteady rotating flows of a generalized Maxwell fluid with oscillating pressure gradient between coaxial cylinders

This paper deals with the unsteady rotating flow of a generalized Maxwell fluid with fractional derivative model between two infinite straight circular cylinders, where the flow is due to an infinite straight circular cylinder rotating and oscillating pressure gradient. The velocity field and the adequate shear stress are determined by means of the combine of the sequential fractional derivatives Laplace transform and finite Hankel transform. The exact solutions are presented by integral and series form in terms of the generalized G and Mittag-Leffler functions. The similar solutions can be easily obtained for ordinary Maxwell and Newtonian fluids as limiting cases. Finally, the influence of the relaxation time and the fractional parameter on the fluid dynamic characteristics, as well as a comparison between models, is shown by graphical illustrations.