A computational investigation of a non-singular fractional operator for an unsteady MHD flow problem

This paper analyzes the impacts of thermal conductivity and variable viscosity on unsteady magnetohydrodynamic (MHD) fluid flow over an infinite vertical plate embedded in a porous medium, including thermal diffusion effects. Atangana–Baleanu (AB) and Caputo–Fabrizio (CF) fractional derivatives are applied in this work to model the system, including the effects of nonlocal and nonsingular kernels. A dimensionless formulation of the governing partial differential equations (PDEs) has been established. The equations are then discretized by using the ordinary finite difference approach and then numerically solved by adopting the Gauss-Seidel iteration process. The influences of different parameters involved in the problems have been illustrated graphically and numerically. The variation of AB and CF fractional derivatives is obtained through a MATLAB based computational approach for the different values of velocity, temperature, and concentration distributions with respect to time under various parameters. A tabular comparison between AB and CF methods have been shown. It has been found that both approaches exhibit a significant level of consistency.