  For a class of competition-diffusion nonlinear systems involving fractional
powers of the Laplacian, including as a special case the fractional
Gross-Pitaevskii system, we prove that uniform boundedness implies H\"older
boundedness for sufficiently small positive exponents, uniformly as the
interspecific competition parameter diverges. This implies strong convergence
of the family of solutions as the segregation of their support occurs.
