This paper focuses on the problem of fractional time derivative of fluid flow and convective heat and mass transfer from a heated semi-infinite wall immersed. We provided two cases of study, one is free convective heat transfer and the other is a free double-convective heat and mass transfer. The time-derivative terms in the equations of momentum, energy and concentration are assumed to be fractional using the Grunwald-Letnikov (GL) model. A finite difference scheme has been developed for each case of study and followed by a von Neumann stability analysis. Therefore, a stability condition has been derived for each case of study. It was found that the derived stability condition collapses to the traditional one as the derivative order equals one, which reflects an accurate implementation. Also, selected physical results have been presented for the velocity, temperature and concentration profiles as well as variations of Nusselt/Sherwood number and friction coefficient.