Exact solution on unsteady Couette flow of generalized Maxwell fluid with fractional derivative

In this paper the unsteady Couette flow of a generalized Maxwell fluid with fractional derivative (GMF) is studied. The exact solution is obtained with the help of integral transforms (Laplace transform and Weber transform) and generalized Mittag-Leffler function. It was shown that the distribution and establishment of the velocity is governed by two non-dimensional parameters eta, b and fractional derivative alpha of the model. The result of classical (Newtonian fluid and standard Maxwell fluid) Couette flow can be obtained as a special case of the result given by this paper, and the decaying of the unsteady part of GMF displays power law behavior, which has scale invariance.