  With respect to a class of long-range exclusion processes on $\mathbb{Z}^d$,
with single particle transition rates of order $|\cdot|^{-(d+\alpha)}$,
starting under Bernoulli invariant measure $\nu_\rho$ with density $\rho$, we
consider the fluctuation behavior of occupation times at a vertex and more
general additive functionals. Part of our motivation is to investigate the
dependence on $\alpha$, $d$ and $\rho$ with respect to the variance of these
functionals and associated scaling limits. In the case the rates are symmetric,
among other results, we find the scaling limits exhaust a range of fractional
Brownian motions with Hurst parameter $H\in [1/2,3/4]$.
  However, in the asymmetric case, we study the asymptotics of the variances,
which when $d=1$ and $\rho=1/2$ points to a curious dichotomy between
long-range strength parameters $0<\alpha\leq 3/2$ and $\alpha>3/2$. In the
former case, the order of the occupation time variance is the same as under the
process with symmetrized transition rates, which are calculated exactly. In the
latter situation, we provide consistent lower and upper bounds and other
motivations that this variance order is the same as under the asymmetric
short-range model, which is connected to KPZ class scalings of the space-time
bulk mass density fluctuations.
