  The classical Fokker-Planck equation (FPE) is a key tool in physics for
describing systems influenced by drag forces and Gaussian noise, with
applications spanning multiple fields. We consider the fractional Fokker-Planck
equation (FFPE), which models the time evolution of probability densities for
systems driven by L\'evy processes, relevant in scenarios where Gaussian
assumptions fail. The paper presents an efficient and accurate numerical
approach for the free-space FFPE with constant coefficients and Dirac-delta
initial conditions. This method utilizes the integral representation of the
solutions and enables the efficient handling of very high-dimensional problems
using fast algorithms. Our work is the first to present a high-precision
numerical solver for the free-space FFPE with Dirac-delta initial conditions.
This opens the door for future research on more complex scenarios, including
those with variable coefficients and other types of initial conditions.
