In this paper, we investigate a class of generalized McKean–Vlasov stochastic differential equations driven by time-changed Lévy noise with two drift terms, one driven by the random change \(E_t\) and the other driven by non-random time t. Firstly, we establish some new time-changed Gronwall-like inequalities, which makes it easy to apply in practice and it can be considered as a more general tool in some situations. As applications of those inequalities, we prove the existence and uniqueness of the solution to the considered equations under some non-Lipschitz conditions by employing the Carathéodory approximation. Meanwhile, by developing some generalized Itô’s formula, some sufficient conditions are provided to guarantee the solutions to be stable in several different senses in terms of Lyapunov functions. Subsequently, by using the established new time-changed Gronwall-like inequalities, we show that the solutions of the generalized distribution dependent stochastic differential equations driven by time-changed Brownian motion can be approximated by solutions of the associated averaged stochastic differential equations in mean square convergence. Finally, we provide some examples to illustrate the practical usefulness of our theoretical results.
