We study a coupled fractional mean-field forward–backward stochastic differential equation (MF-FBSDE), in which the coefficients involved could also depend upon the distribution of the solution (X, Y), and which contains a special structure $\eta$. We prove the existence and uniqueness of a solution of the fractional MF-FBSDE by using the method of continuation.

中文翻译：

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耦合分数平均场正反向随机微分方程解的存在唯一性

我们研究了一个耦合分数平均场正反向随机微分方程 (MF-FBSDE)，其中所涉及的系数也可能取决于解 ( X, Y ) 的分布，并且包含一个特殊的结构 $\eta$. 我们用延拓法证明了分数阶MF-FBSDE解的存在唯一性。