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The prime objective of the present article is to investigate the heat and mass transfer impact on the viscous chemically reacting transient fluid flow past an upright surface analytically by employing Prabhakar fractional model. The fractional model has been developed for investigating the transient viscous fluid flow in the presence of inclined magnetic force subject to Newtonian surface heating. The integer order computation techniques for the governing partial differential equations for the formulated flow problem fail to determine the physical behavior of flow parameters with memory effects. To this end, the present model presents the fractional approach based on the Prabhakar fractional derivative. The problem modeled in terms of dimensionless expressions is first transformed into fractional model and later on simulations are performed with Laplace technique. The inverse Laplace transform of the flow characteristics is computed by adopting Stehfest and Tzou’s algorithms. For fractional parameters, the increasing trend in the velocity and temperature profiles has been observed. The increasing behavior of velocity subject to increasing values of heat Grashof number and mass Grashof number is observed.

Prabhakar fractional model for viscous transient fluid with heat and mass transfer and Newtonian heating applications