Partial slip effects on the oscillatory flows of a fractional Jeffrey fluid in a porous medium

The exact analytical solutions are obtained for three basic fluid flow problems in a porous medium when the no-slip condition is no longer valid. The fractional calculus approach is used to describe the constitutive model of a magnetohydrodynamic fractional Jeffrey fluid. The porous medium is taken into account using modified Darcy's law for fractional viscoelastic fluid The effects of Hall current are also taken into account. A parametric study of some physical parameters involved in the problem is performed to illustrate the influence of these parameters on the velocity profiles. In each case, the analytical solutions are obtained using Fourier transform for fractional calculus. The solutions for the no-slip condition are special cases of the presented analysis. The critical assessment is made for the cases of partial slip and no-slip conditions. Moreover the well-known solutions for a Newtonian fluid in nonporous and porous media are limiting cases of our solutions.