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It is looked into how fractional MHD and viscous fluid naturally flow across a vertical plate that oscillates with a steady heat flux in a porous medium. The analytical solution for non-dimensional momentum was generated using the Laplace transform and the Boussinesq approximation. Comparisons are presented between Fourier’s law-described classical thermal transport and Prabhakar-like fractional time free convection flows in terms of temperature and velocity. By using fractional viscous fluid, we were able to produce conventional viscous fluid solutions and complete their objective. Finally, diagrams are used to show how different parameters such as Prandtl number, fractional parameters, Grashof number, effective permeability, time on temperature and velocity, and graphically recovered the solution available in the literature.