Abstract
The unsteady natural convection flow for the maxwell fluid due to infinite plate is inspected with help off ractional derivatives. The effects of slip conditions, Newtonian heating effect, MHD, and radiation are also considered. The recent definitions of fractional derivatives i.e. Atangana-Baleanu (AB) and Caputo-Fabrizio (CF) fractional derivatives are used to construct the fractional modal of leading partial differential equations. The semi-analytical solution of the governing equations is attained by utilizing the Laplace transformation and some numerical techniques i.e. Stehfest and Tzou's algorithms. Moreover, to analyze the physical significance of the under consideration problem, the graphical analysis is explored. The results concluded that the temperature and velocity profile obtained via CF-fractional derivative shows a declining trend when compared with AB-fractional derivative. Furthermore, the velocity and temperature fields were also decayed by varying the value of fractional parameters in both AB and CF cases.