Analysis of magnetohydrodynamic flow of a fractional viscous fluid through a porous medium

The aim of this paper is to investigate the exact general solutions of the incompressible viscous fluid flow by using the time-fractional Caputo-Fabrizio derivative. The flow of the fluid is subject to the motion of a plane wall, embedded in a porous medium under the influence of magnetic field. The corresponding non-dimensional governing fractional differential equation with appropriate initial and boundary conditions is solved by means of integral transforms namely, Laplace and Fourier transforms. Solutions are expressed as a sum of steady and transient parts, for the sinusoidal oscillations of the plane wall. The influence of involved physical parameters are discussed graphically. Specifically, it has been observed that the effective permeability Keff reduces the time taken to reach the steady state.