  We consider a time dependent problem generated by a nonlocal operator in
space. Applying a discretization scheme based on $hp$-Finite Elements and a
Caffarelli-Silvestre extension we obtain a semidiscrete semigroup. The
discretization in time is carried out by using $hp$-Discontinuous Galerkin
based timestepping. We prove exponential convergence for such a method in an
abstract framework for the discretization in the original domain $\Omega$.
