  In this paper we study a class of stochastic partial differential equations
in the whole space $\mathbb{R}^{d}$, with arbitrary dimension $d\geq 1$, driven
by a Gaussian noise white in time and correlated in space. The differential
operator is a fractional derivative operator. We show the existence, uniqueness
and H\"{o}lder's regularity of the solution. Then by means of Malliavin
calculus, we prove that the law of the solution has a smooth density with
respect to the Lebesgue measure.
