  Applying ideas of fractional analogue of Monge-Amp\'ere operator by L.
Caffarelli and F. Charro, we consider an analogue of fractional k-Hessian
operators expressed as concave envelopes of fractional linear operators, and
reproduce the same regularity results when k=2.
  Under the set up of global solutions prescribing data at infinity and global
barriers, the key estimate is to prove that fractional 2-Hessian operator is
strictly elliptic. Then we can apply nonlocal Evans-Krylov theorem to prove
such solutions are classical.
