In this paper, we study McKean–Vlasov stochastic differential equations driven by fractional stable processes \(\begin{aligned} dX_t=b(t,X_t,\mathcal {L}_{X_t})dt+\sigma (t, \mathcal {L}_{X_t})dZ_t^{H,\alpha }, \end{aligned}\) where \(\mathcal {L}_{X_t}\) denotes the law of \(X_t\) , \(\{Z_t^{H,\alpha }, t\in [0,T]\}\) is a fractional stable process with parameters \(\alpha \in (1,2)\) and \(H\in (1/\alpha ,1)\) . We establish the existence and uniqueness theorem for solutions of these type of equations, and then give the theory of chaos propagation. Moreover, we show that the solutions can be approximated by the solutions of the associated averaged McKean–Vlasov stochastic differential equations in the sense of moment convergence, and provide an example of numerical simulation. These results not only generalize the corresponding results about stable processes to fractional stable processes, but also extend the fractional Brownian motion case to the non-Gaussian case.
