  Time fractional PDEs have been used in many applications for modeling and
simulations. Many of these applications are multiscale and contain high
contrast variations in the media properties. It requires very small time step
size to perform detailed computations. On the other hand, in the presence of
small spatial grids, very small time step size is required for explicit
methods. Explicit methods have many advantages as we discuss in the paper. In
this paper, we propose a partial explicit method for time fractional PDEs. The
approach solves the forward problem on a coarse computational grid, which is
much larger than spatial heterogeneities, and requires only a few degrees of
freedom to be treated implicitly. Via the construction of appropriate spaces
and careful stability analysis, we can show that the time step can be chosen
not to depend on the contrast or scale as the coarse mesh size. Thus, one can
use larger time step size in an explicit approach. We present stability theory
for our proposed method and our numerical results confirm the stability
findings and demonstrate the performance of the approach.
