  In this paper we study a class of distribution dependent stochastic
differential equations driven by fractional Brownian motions with Hurst
parameter H\in(1/2,1). We prove the well-posedness of this type equations, and
then establish a general result on the Bismut formula for the Lions derivative
by using Malliavin calculus. As applications, we provide the Bismut formulas of
this kind for both non-degenerate and degenerate cases, and obtain the
estimates of the Lions derivative and the total variation distance between the
laws of two solutions.
