Influence of Hall current on the flows of a generalized Oldroyd-B fluid in a porous space

Exact analytical solutions for the magnetohydrodynamic (MHD) flows of an Oldroyd-B fluid through a porous space are developed. The fractional calculus approach is used to describe the constitutive model of a generalized Oldroyd-B fluid. The porous space is taken into account using modified Darcy's law for fractional viscoelastic fluid. The effect of Hall current is taken into account. Some interesting flows induced due to certain special oscillations are given. In each case, the analytical solutions are obtained using Fourier transform for fractional calculus. The present analysis with fractional calculus approach seems a first attempt for the study of MHD viscoelastic flows in a porous medium.