An exponentially convergent discretization for space-time fractional parabolic equations using hp-FEM

We consider a space-time fractional parabolic problem. Combining a sinc quadrature-based method for discretizing the Riesz-Dunford integral with hp-FEM in space yields an exponentially convergent scheme for the initial boundary value problem with homogeneous right-hand side. For the inhomogeneous problem, an hp-quadrature scheme is implemented. We rigorously prove exponential convergence with focus on small times t, proving robustness with respect to startup singularities due to data incompatibilities.