  We study the existence of a unique solution to semilinear fractional backward
doubly stochastic differential equation driven by a Brownian motion and a
fractional Brownian motion with Hurst parameter less than 1/2. Here the
stochastic integral with respect to the fractional Brownian motion is the
extended divergence operator and the one with respect to Brownian motion is
It\^o's backward integral. For this we use the technique developed by
R.Buckdahn to analyze stochastic differential equations on the Wiener space,
which is based on the Girsanov theorem and the Malliavin calculus, and we
reduce the backward doubly stochastic differential equation to a backward
stochastic differential equation driven by the Brownian motion. We also prove
that the solution of semilinear fractional backward doubly stochastic
differential equation defines the unique stochastic viscosity solution of a
semilinear stochastic partial differential equation driven by a fractional
Brownian motion.
