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Decay of potential vortex for a viscoelastic fluid with fractional Maxwell model. (English) Zbl 1185.76523
Summary: This paper is concerned with the exact analytic solutions for the velocity field and the associated tangential stress corresponding to a potential vortex for a fractional Maxwell fluid. The fractional calculus approach is taken into account in the constitutive relationship of a non-Newtonian fluid model. Exact analytic solutions are obtained by using the Hankel transform and the discrete Laplace transform of sequential fractional derivatives. The solutions for a Maxwell fluid appear as the limiting cases of our general solutions by setting $\alpha =1$. The influence of fractional coefficient on the decay of vortex velocity is also analyzed by graphical illustrations.
##### MSC:
 76D17 Viscous vortex flows 26A33 Fractional derivatives and integrals (real functions)