  We provide some equations for the Variance Gamma process due to the fact that
we do not consider only the definition as a time-changed Brownian motion. This
brings us to a new non-local equation, even true in the drifted case, involving
generalized Weyl derivatives. Then we focus on the connection to special
functions and we study a space equation for our process. At the end, we
conclude by observing the convergence in distribution of a compound Poisson
process to the Variance Gamma process.
