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New exact solutions are obtained for unsteady magnetohydrodynamic (MHD) flows of a generalized second-grade fluid near a uniform accelerating plate. The generalized second-grade fluid saturates the porous space. A fractional derivative is used in the governing equation. Analytical expressions for the velocity and shear stress fields are obtained by using the Laplace transform technique for fractional calculus. The obtained solutions are expressed in the series form in terms of Fox  H -functions. Similar solutions for an ordinary second-grade fluid passing through a porous space are also derived. Moreover, several graphs are constructed for the pertinent parameters to analyze the characteristics of the velocity and shear stress field.

A hydromagnetic flow through porous medium near an accelerating plate in the presence of magnetic field