  We provide sharp error bounds for the difference between the transition
densities of some multidimensional Continuous Time Markov Chains (CTMC) and the
fundamental solutions of some fractional in time Partial (Integro) Differential
Equations (P(I)DEs). Namely, we consider equations involving a time fractional
derivative of Caputo type and a spatial operator corresponding to the generator
of a non degenerate Brownian or stable driven Stochastic Differential Equation
(SDE).
