Conditional McKean–Vlasov stochastic differential equations driven by fractional Brownian motions

In this paper, we are concerned with a class of McKean–Vlasov stochastic differential equations with Markovian regime-switching driven by fractional Brownian motions with Hurst parameter $H>\frac{1}{2}$. We first obtain the existence and uniqueness theorem for solutions of the concerned equations under the non-Lipschitz conditions. Second, we establish the propagation of chaos for the associated mean-field interaction particle systems with common noise and provide an explicit bound on the convergence rate. At last, an averaging principle is investigated with respect to two time-scale conditional McKean–Vlasov stochastic differential equations.