  This work is concerned with the existence of mild solutions and the
uniqueness of distributional solutions to nonlinear Fokker-Planck equations
with nonlocal operators $\Psi(-\Delta)$, where $\Psi$ is a Bernstein function.
As applications, the existence and uniqueness of solutions to the corresponding
nonlinear martingale problems are proved. Furthermore, it is shown that these
solutions form a nonlinear Markov process in the sense of McKean such that
their one-dimensional time marginal law densities are the solutions to the
nonlocal nonlinear Fokker-Planck equation. Hence, McKean's program envisioned
in his PNAS paper from 1966 is realized for these nonlocal PDEs.
