Limiting Behavior of Solutions to Mckean–Vlasov Fractional Sdes With HöLder Diffusion Coefficients

ABSTRACT In this paper, we investigate the limiting behavior of solutions for a class of Itô–Doob fractional stochastic differential equations (SDEs) with distribution‐dependent (McKean–Vlasov) and Hölder diffusion coefficients, using the averaging principle. The work in the article is roughly divided into three parts. Firstly, we establish a generalized Grönwall inequality with singular integral kernel to suit the needs of this paper. Secondly, utilizing the Yamada–Watanabe approximation method and iterative techniques, we provide results on the existence and uniqueness of a strong solution to the equation. Finally, we discuss the convergence result in mean square sense between the solutions of the original equation and the averaged equation.