  After reviewing the problematic behavior of some previously suggested finite
interval spatial operators of the symmetric Riesz type, we create a wish list
leading toward a new spatial operator suitable to use in the space-time
fractional differential equation of anomalous diffusion when the transport of
material is strictly restricted to a bounded domain. Based on recent studies of
wall effects, we introduce a new definition of the spatial operator and
illustrate its favorable characteristics. We provide two numerical methods to
solve the modified space-time fractional differential equation and show
particular results illustrating compliance to our established list of
requirements, most important to the conservation principle and the second law
of thermodynamics.
