Applications of Prabhakar-like Fractional Derivative for the Solution of Viscous Type Fluid with Newtonian Heating Effect

Abstract

This article examines a natural convection viscous unsteady fluid flowing on an oscillating infinite inclined plate. The Newtonian heating effect, slip effect on the boundary wall, and constant mass diffusion conditions are also considered. In order to account for extended memory effects, the semi-analytical solution of transformed governed partial differential equations is attained with the help of a recent and more efficient fractional definition known as Prabhakar, like a thermal fractional derivative with Mittag-Leffler function. Fourier and Fick’s laws are also considered in the thermal profile and concentration field solution. The essentials’ preliminaries, fractional model, and execution approach are expansively addressed. The physical impacts of different parameters on all governed equations are plotted and compared graphically. Additionally, the heat transfer rate, mass diffusion rate, and skin friction are examined with different numerical techniques. Consequently, it is noted that the variation in fractional parameters results in decaying behavior for both thermal and momentum profiles while increasing with the passage of time. Furthermore, in comparing both numerical schemes and existing literature, the overlapping of both curves validates the attained solution of all governed equations.