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In this paper, we first study the well-posedness of a class of McKean-Vlasovstochastic partial differential equations driven by cylindrical $\alpha$-stableprocess, where $\alpha\in(1,2)$. Then by the method of the Khasminskii's timediscretization, we prove the averaging principle of a class of multiscaleMcKean-Vlasov stochastic partial differential equations driven by cylindrical$\alpha$-stable processes. Meanwhile, we obtain a specific strong convergencerate.

Well-posedness and averaging principle of McKean-Vlasov SPDEs driven by cylindrical $\alpha$-stable process