In this paper, we study a new class of equations called mean-field backward stochastic differential equations (BSDEs, for short) driven by fractional Brownian motion with Hurst parameter H > 1/2. First, the existence and uniqueness of this class of BSDEs are obtained. Second, a comparison theorem of the solutions is established. Third, as an application, we connect this class of BSDEs with a nonlocal partial differential equation (PDE, for short), and derive a relationship between the fractional mean-field BSDEs and PDEs.

中文翻译：

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分数布朗运动驱动的平均场向后随机微分方程

在本文中，我们研究了一类新的方程，称为平均场后向随机微分方程（简称 BSDE），由 Hurst 参数H > 1/2 的分数布朗运动驱动。首先，得到该类BSDE的存在性和唯一性。其次，建立了解的比较定理。第三，作为一个应用，我们将这类BSDEs与一个非局部偏微分方程（简称PDE）联系起来，推导出分数平均场BSDEs和PDEs之间的关系。