  In this paper, we study small-time asymptotic behaviors for a class of
distribution dependent stochastic differential equations driven by fractional
Brownian motions with Hurst parameter $H\in(1/2,1)$ and magnitude $\ep^H$. By
building up a variational framework and two weak convergence criteria in the
factional Brownian motion setting, we establish the large and moderate
deviation principles for this type equations. Besides, we also obtain the
central limit theorem, in which the limit process solves a linear equation
involving the Lions derivative of the drift coefficient.
