We investigated the Hall and ion slip effects on the MHD convective flow of elastico-viscous fluid through porous medium between two rigidly rotating parallel plates with time fluctuating sinusoidal pressure gradient in this paper. In an initially undisturbed state both the fluid and the plates are in rigid rotation with the uniform angular velocity Ω about the normal to the plates. At t > 0 the fluid is driven by a fluctuating pressure gradient parallel to the channel walls. Analytical solutions for the velocity, temperature and concentration are evaluated and discussed computationally with the help of graphical profiles. For engineering interest, we obtained skin friction , Nusselt number , Sherwood number and volumetric flow rate and discussed numerically. Elasticity and magnetic field resist the fluid motion gets thinner boundary layer. Lesser frequency of oscillating pressure gradient frightens the reverse flow. The similar variation of skin friction should be circumvented with less significant time span and strength of the magnetic field .