Numerical analysis of time-fractional MHD prandtl fluid flow in porous media using radial basis functions and Crank–Nicolson scheme

In this study, the magnetohydrodynamic (MHD) flow of a Prandtl fluid through a porous medium confined between two parallel plates is investigated. The lower plate is stationary, while the upper plate exhibits oscillatory motion. A novel numerical approach is employed, combining radial basis function (RBF) collocation with the Crank–Nicolson scheme to solve the time-fractional partial differential equation governed by the Caputo fractional derivative. The method’s robustness and accuracy are demonstrated through detailed numerical results, emphasizing the influence of key parameters such as the MHD parameter, Prandtl fluid parameter, porous medium parameter and fractional derivative orders. Graphical illustrations highlight the dynamic interplay between these parameters and the fractional behavior, offering deeper insights into the impact of fractionality on fluid flow characteristics.