Fractional magnetohydrodynamics oldroyd-B fluid over an oscillating plate

Abstract

This paper presents some new exact solutions corresponding to the oscillating flows of a magnetohydrodynamic Oldroyd-B fluid with fractional derivatives. The fractional calculus approach in the governing equations is used. The exact solutions for the oscillating motions of a fractional magnetohydrodynamic Oldroyd-B fluid due to sine and cosine oscillations of an infinite plate are established with the help of discrete Laplace transform. The expressions for velocity field and the associated shear stress that have been obtained, presented in series form in terms of Fox H-functions, satisfy all imposed initial and boundary conditions. Similar solutions for ordinary magnetohydrodynamic Oldroyd-B, fractional and ordinary magnetohydrodynamic Maxwell, fractional and ordinary magnetohydrodynamic second grade and magnetohydrodynamic Newtonian fluid as well as those for hydrodynamic fluids are obtained as special cases of general solutions. Finally, the obtained solutions are graphically analyzed through various parameters of interest.