  We consider a general family of nonlocal in space and time diffusion
equations with space-time dependent diffusivity and prove convergence of finite
difference schemes in the context of viscosity solutions under very mild
conditions. The proofs, based on regularity properties and compactness
arguments on the numerical solution, allow to inherit a number of interesting
results for the limit equation. More precisely, assuming H\"older regularity
only on the initial condition, we prove convergence of the scheme, space-time
H\"older regularity of the solution depending on the fractional orders of the
operators, as well as specific blow up rates of the first time derivative.
Finally, using the obtained regularity results, we are able to prove orders of
convergence of the scheme in some cases. These results are consistent with
previous studies. The schemes' performance is further numerically verified
using both constructed exact solutions and realistic examples. Our experiments
show that multithreaded implementation yields an efficient method to solve
nonlocal equations numerically.
