Stochastic averaging principle for two-time-scale SPDEs driven by fractional Brownian motion with distribution dependent coefficients

In this paper, we aim to study the asymptotic behavior for a class of distribution dependent stochastic partial differential equations (SPDEs) driven by fractional Brownian motion with fast and slow time-scales. We first establish the well-posedness of distribution dependent SPDEs driven by fractional Brownian motion under the non-Lipschitz conditions using Carathéodory approximation. Then, using classical Khasminskii time discretization, we establish that stochastic averaging principle for a class of fast and slow system of distribution dependent SPDEs driven by fractional Brownian motion.