Department of Mathematics, University of Malakand, Chakdara, Khyber Pakhtunkhwa, 18000, Pakistan
New exact solutions for unsteady magnetohydrodynamic (MHD) ﬂows of a generalized second-grade ﬂuid due to uniform accelerating plate are derived. The generalized second-grade ﬂuid saturates the porous space. Fractional derivative is used in the governing equation. The analytical expressions for velocity and shear stress ﬁelds are obtained by using Laplace transform technique for the fractional calculus. The obtained solutions are expressed in series form in terms of Fox H-functions. Similar solutions for ordinary second-grade ﬂuid passing through a porous space are also recovered. Moreover, several ﬁgures are sketched for the pertinent parameters to analyze the characteristics of velocity ﬁeld and shear stress.