  We introduce a system of fractional nonlinear Schroedinger equations (FNLSEs)
which model the copropagation of optical waves carried by different wavelengths
or mutually orthogonal circular polarizations in fiber-laser cavities with the
effective fractional group-velocity dispersion (FGVD), which were recently made
available to the experiment. In the FNLSE system, the FGVD terms are
represented by the Riesz derivatives, with the respective Levy index (LI). The
FNLSEs, which include the nonlinear self-phase-modulation (SPM) nonlinearity,
are coupled by the cross-phase modulation (XPM) terms, and separated by a
group-velocity (GV) mismatch (rapidity). By means of systematic simulations, we
analyze collisions and bound states of solitons in the XPM-coupled system,
varying the LI and GV mismatch. Outcomes of collisions between the solitons
include rebound, conversion of the colliding single-component solitons into a
pair of two-component ones, merger of the solitons into a breather, their
mutual passage leading to excitation of intrinsic vibrations, and the elastic
interaction. Families of stable two-component soliton bound states are
constructed too, featuring a rapidity which is intermediate between those of
the two components.
