Decay of a potential vortex in a generalized Oldroyd-B fluid

The velocity field and the adequate shear stress corresponding to the decay of a potential vortex in a generalized Oldroyd-B fluid are determined by means of Hankel and Laplace transforms. The exact solutions, written in terms of the generalized G and R functions, are presented as a sum of the Newtonian solutions and the adequate non-Newtonian contributions. These solutions can be easy specialized to give the solutions for generalized Maxwell fluids and ordinary Oldroyd-B or Maxwell fluids performing the same motion. The influence of the fractional parameters as well as that of the material parameters on the decay of the vortex is emphasized by graphical illustrations.