  In this paper we study the Large Deviation Principle (LDP in abbreviation)
for a class of Stochastic Partial Differential Equations (SPDEs) in the whole
space $\mathbb{R}^d$, with arbitrary dimension $d\geq 1$, under random
influence which is a Gaussian noise, white in time and correlated in space. The
differential operator is a fractional derivative operator. We prove a large
deviations principle for our equation, using a weak convergence approach based
on a variational representation of functionals of infinite-dimensional Brownian
motion. This approach reduces the proof of LDP to establishing basic
qualitative properties for controlled analogues of the original stochastic
system.
