In this paper, we are concerned with the following generalized fully nonlinear nonlocal operators:
$ F_{s,m}(u(x)) = c_{N,s} m^{ \frac{N}{2}+s} P.V. \int_{\mathbb{R}^{N}} \frac{G(u(x)-u(y))}{|x-y|^{ \frac{N}{2}+s}} K_{ \frac{N}{2}+s}(m|x-y|)dy+m^{2s}u(x), $
where $ s\in (0,1) $ and mass $ m>0 $. By establishing various maximal principle and using the direct method of moving plane, we prove the monotonicity, symmetry and uniqueness for solutions to fully nonlinear nonlocal equation in unit ball, $ \mathbb{R}^{N} $, $ \mathbb{R}^{N}_{+} $ and a coercive epigraph domain $ \Omega $ in $ \mathbb{R}^N $ respectively.
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