Exact solutions for rotational flow of a fractional Maxwell fluid in a circular cylinder

This paper deals with the rotational flow of a fractional Maxwell fluid in an infinite circular cylinder, due to the torsional variable time-dependent shear stress that is prescribed on the boundary of the cylinder. The fractional calculus approach in the constitutive relationship model of a Maxwell fluid is introduced. The velocity field and the resulting shear stress are determined by means of the Laplace and finite Hankel transforms to satisfy all imposed initial and boundary conditions. The solutions corresponding to ordinary Maxwell fluids as well as those for Newtonian fluids, performing the same motion, are obtained as limiting cases of our general solutions. Finally, the influence of the relaxation time and the fractional parameter on the velocity of the fluid is analyzed by graphical illustrations