### Effect of General Non-Slip Condition and MHD on Accelerated Flows of a Viscoelastic Fluid With the Fractional Burgers' Model

#### Abstract

In this paper, the effect of general non-slip condition and magnetohydrodynamic (MHD) on accelerated flows of a viscoelastic fluid with the fractional Burgers’ model are studied. The velocity field of the flow is described by a fractional partial differential equation. By using Fourier sine transform and Laplace transform, exact solutions for the velocity distribution and shear stress are obtained for flow induced by variable accelerated plate. These solutions, are presented under integral and series forms in terms of the generalized Mittag-Leffler function, as the sum of two terms. The first term represents the velocity field corresponding to a Newtonian fluid, and the second term gives the non-Newtonian contributions to the general solutions. The similar solutions for second grad, Maxwell and Oldroyd-B fluids with fractional derivatives as well as those for the ordinary models are obtained as the limiting cases of our solutions. Moreover, in the special cases when 1, as it was to be expected, our solutions tend to the similar solutions for an ordinary Burgers’ fluid. While the MATHEMATICA package is used to draw the figures velocity components in the plane.

#### Metrics