This presentation will report a recent generalization of the Navier-Stokes-Euler governing equations of fluid flow to fractional time and multi-fractional space. In the case their fractional powers in time and in multi-fractional space are specified to integer values, the developed fractional continuity and momentum equations of fluid flow reduce to the classical Navier-Stokes-Euler equations. The developed fractional governing equations of fluid flow are nonlocal in time and space. As such, they can quantify the effects of initial and boundary conditions on a flow process at long times after the initial time and long distances after the upstream boundary locations. As such, these equations have potential in simulating flow processes with long memories in time and space. The numerical simulations with the developed equations show that these equations are capable of simulating anomalous sub and super diffusion behaviors. In the presentation the fractional governing equations will be explained and their numerical applications will be discussed.
