This paper presents a study for the influence of magnetohydrodynamic (MHD) on the oscillating flows of fractional Burgers’ fluid. The fractional calculus approach in the constitutive relationship model is introduced and a fractional Burgers’ model is built. The exact solution of the oscillating motions of a fractional Burgers’ fluid due to cosine and sine oscillations of an infinite flat plate are established with the help of integral transforms (Fourier sine and Laplace transforms). The expressions for the velocity field and the resulting shear stress that have been obtained, presented under integral and series form in terms of the generalized Mittag-Leffler function, satisfy all imposed initial and boundary conditions. Finally, the obtained solutions are graphically analyzed for variations of interesting flow parameters. While the MATHEMATICA package is used to draw the figures velocity components in the plane.
