We study the fractional diffusion in a Gaussian noisy environment as
described by the fractional order stochastic partial equations of the following
form: Dtαu(t,x)=Bu+u⋅WH, where Dtα is the
fractional derivative of order α with respect to the time variable t,
B is a second order elliptic operator with respect to the space
variable x∈Rd, and WH a fractional Gaussian noise of Hurst
parameter H=(H1,⋯,Hd). We obtain conditions satisfied by α
and H so that the square integrable solution u exists uniquely