  Levy walks define a fundamental concept in random walk theory which allows
one to model diffusive spreading that is faster than Brownian motion. They have
many applications across different disciplines. However, so far the derivation
of a diffusion equation for an n-dimensional correlated Levy walk remained
elusive. Starting from a fractional Klein-Kramers equation here we use a moment
method combined with a Cattaneo approximation to derive a fractional diffusion
equation for superdiffusive short range auto-correlated Levy walks in the large
time limit, and solve it. Our derivation discloses different dynamical
mechanisms leading to correlated Levy walk diffusion in terms of quantities
that can be measured experimentally.
