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We first state a special type of It\^o formula involving stochastic integralsof both standard and fractional Brownian motions. Then we use Doss-Sussmantransformation to establish the link between backward doubly stochasticdifferential equations, driven by both standard and fractional Brownianmotions, and backward stochastic differential equations, driven only bystandard Brownian motions. Following the same technique, we further studyassociated nonlinear stochastic partial differential equations driven byfractional Brownian motions and partial differential equations with stochasticcoefficients.

Nonlinear Fractional Backward Doubly Stochastic Differential Equations with Hurst Parameter in (1/2,1)