  In this article a fractional cross-diffusion system is derived as the
rigorous many-particle limit of a multi-species system of moderately
interacting particles that is driven by L\'{e}vy noise. The form of the mutual
interaction is motivated by the porous medium equation with fractional
potential pressure. Our approach is based on the techniques developed by
Oelschl\"ager (1989) and Stevens (2000), in the latter of which the convergence
of a regularization of the empirical measure to the solution of a
correspondingly regularized macroscopic system is shown. A well-posedness
result and the non-negativity of solutions are proved for the regularized
macroscopic system, which then yields the same results for the non-regularized
fractional cross-diffusion system in the limit.
