Abstract
The emergence of Atangana–Baleanu fractional derivative in solving various physical phenomenon is extraordinarily beneficial and provide results that are more realistic. Therefore, this article focused on the application of this fractional operator to magnetohydrodynamic (MHD) movement of second-grade fluid in an inclined heated plate with an inclined magnetic field. The problem is constructed in terms of fractional PDE's subject to physical initial and boundary conditions. The solutions are obtained by the joint application of Laplace and Zakian's numerical algorithm. To explore the effect of various flow parameters, the solutions are plotted in graphs and discussed physically. It is found that the fluid velocity decreases with an increasing fractional parameter α. For α=1, the fluid velocity is minimum. Furthermore, it is explored that the strength of the magnetic field is strongest for the inclination angle β=π2.