The free convective unsteady fluctuating, MHD flow of electrically conducting viscoelastic dusty fluid in a channel-driven with the impact of oscillating pressure gradient and the motion of the upper plate has been studied in this article. The noteworthy heat generation/absorption has also taken into account, the heat generation established the mechanism of heat transfer by both the momentum of fluid and the motion of dust particle and absorption of heat by the dust particle is because of conduction. The coupled governing partial differential equations are reduced to the ordinary differential equation through the assumed periodic solutions. Analytical solutions for the velocity of the fluid as well as the velocity of dust particles and for energy equation of the fluid and for dust particles are obtained by using Poincare-Light Hill Perturbation Technique. The influence of various parameters of interest is discussed on the velocity and temperature profiles of the fluid and particles. The evolution of fluid-phase and dusty-phase with dual behavior of the magnetic parameter for both boundary layer and free stream velocities has been discussed. The boundary layer velocity decreased with an increase in magnetic parameter, while at the free stream flow, the result is quite opposite. The above result of magnetic field is worthwhile and can be used to control the boundary layer thickness. The current work also concludes that by increasing the Peclet number and concentration of the dust particles retards the boundary layer velocity. Furthermore, various physical parameters like coefficient of heat absorption, concentration of the dust particles, peclet number, magnetic parameter, and temperature relaxation time parameter retard the motion of dusty-phase, while Grashof number enhances the flow of dusty-phase. Other properties of fluid, which have great importance for engineers are, the rate of heat transfer and skin friction. It is shown in Table 1 that by increasing the value of Peclet number from 1 to 2 it increases the rate of heat transfer from 1.3263 to 1.3387. Furthermore, Table 2 shows that by increasing the concentration parameter from 2 to 4 the skin friction increases from 2.3872 to 4.7799.