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The nanoparticles reduce heat dissipation during the solidification and combustion process, this is because the dispersion of nanoparticles accelerates the solidification processes. In this paper, the comparative study of an unsteady free convection MHD flow of nanofluids through an accelerated long vertical plate placed in a porous medium with embedded nanoparticles is proposed for solidification trends. The flow is confined to a moving plate under the inclined magnetic field and affected by chemical reactions, Newtonian heating, and thermal radiation. The governing equations for concentration, temperature, and velocity are reduced in dimensionless and fractionalized with innovative fractional derivatives of Caputo-Fabrizio and Atangana-Baleanu. The Laplace transform is employed on governing equations based on water as base fluid with nanoparticles. The numerical inversion technique, namely the Zakian method, is used. The results suggest the decaying behavior of velocity and temperature with both fractional models based on the memory of the flow at a specific time. [ABSTRACT FROM AUTHOR]