Abstract
Sequel to the significance of the dynamics of second-grade fluid in the industry, nothing is known on the increasing inclined magnetic force, Newtonian heating, slip flow and Prabhakar-like fractional kind of Newtonian heating. In this study, the novel modified and efficient fractional approach, namely, the Prabhakar fractional technique is applied on an unsteady flow of second-grade liquid flowing on an inclined oscillating plate. The flowing fluid is moving under the effects of an applied inclined magnetic field, furthermore, the Newtonian heating effect and slip on the boundaries of the wall are also considered in the boundary conditions. After nondimensionalizing the governing equations, the solution of coupled equations is attained with the help of integral transform i.e., Laplace transformation method, and some numerical approaches are also applied for the Laplace inverse. The results convey that the momentum field decrease with increase in fractional constraints. The thermal change exhibits a declining tendency for increased values of fractional parameters. Furthermore, in comparison of velocity field attained by our applied fractional system with the existing literature, the curves of both Stehfest and Tzou's methods overlay with each other which signifies the validity of our attained outcomes of momentum profile.