  The exclusion process in which particles may jump any distance l>=1 with the
probability that decays as l^-(1+sigma) is studied from coarse-grained equation
for density profile in the limit when the lattice spacing goes to zero. For
1<sigma<2, the usual diffusion term of this equation is replaced by the
fractional one, which affects dynamical-scaling properties of the late-time
approach to the stationary state. When applied to an open system with totally
asymmetric hopping, this approach gives two results: first, it accounts for the
sigma-dependent exponent that characterizes the algebraic decay of density
profile in the maximum-current phase for 1<sigma<2, and second, it shows that
in this region of sigma the exponent is of the mean-field type.
