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An analysis is carried out to study laminar MHD convection flow of a second order dusty viscoelastic fluid in porous medium through an inclined parallel plate channel in the presence of molecular diffusivity. The plates are maintained at two different temperatures that decay with time. The study is done under the consideration that viscosity and density of the fluid are variable to the extent that it causes stratification and joule heating effect in the process of the flow. The purpose of the study is to examine how stratification and joule heating affect the flow in relation to the physical quantities namely, Stratification factor, Hartmann number, Viscoelastic coefficient, Joule heating parameter, Prandtl number, Eckert number, Schmidt number and Porosity of the medium etc. The non-dimensional governing equations are solved analytically by using regular perturbation technique, and the graphs are plotted using MATLAB programming language. The mathematical expressions for fluid and particle velocity, fluid temperature, fluid concentration, skin friction for fluid and particle, flow flux for fluid and particle, Nusselt number, Sherwood number at the plates are evaluated and their nature of variations for different numerical values of physical parameters are shown graphically, discussed and conclusions are drawn.