  This paper devoted to study of fractional elliptic equations driven a
multiplicative noise. By combining the eigenfunction expansion method for
symmetry elliptic operators, the variation of constant formula for strong
solutions to scalar stochastic fractional differential equations, Ito's formula
and establishing a new weighted norm associated with a Lyapunov-Perron operator
defined from this representation of solutions, we show the asymptotic behaviour
of solutions to these systems in mean square sense. As a consequence, we also
prove existence, uniqueness and the convergence rate of their solutions.
