  We first state a special type of It\^o formula involving stochastic integrals
of both standard and fractional Brownian motions. Then we use Doss-Sussman
transformation to establish the link between backward doubly stochastic
differential equations, driven by both standard and fractional Brownian
motions, and backward stochastic differential equations, driven only by
standard Brownian motions. Following the same technique, we further study
associated nonlinear stochastic partial differential equations driven by
fractional Brownian motions and partial differential equations with stochastic
coefficients.
