# Existence Solution for Fractional Mean-Field Backward Stochastic Differential Equation with Stochastic Linear Growth Coefficients

### Abstract

We deal with fractional mean field backwardWe deal with fractional mean field backward stochastic differential equations with hurst parameter $H\in (\frac{1}{2},1)$ when the coefficient $f$ satisfy a stochastic Lipschitz conditions, we prove the existence and uniqueness of solution and provide a comparison theorem. Via an approximation and comparison theorem, we show the existence of a minimal solution when the drift satisfies a stochastic growth condition.

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*MENDEL*. 29, 2 (Dec. 2023), 211-219. DOI:https://doi.org/10.13164/mendel.2023.2.211.

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