  This paper is concerned with the large deviation principle of the non-local
fractional stochastic reaction-diffusion equation with a polynomial drift of
arbitrary degree driven by multiplicative noise defined on unbounded domains.
We first prove the strong convergence of the solutions of a control equation
with respect to the weak topology of controls, and then show the convergence in
distribution of the solutions of the stochastic equation when the noise
intensity approaches zero. We finally establish the large deviations of the
stochastic equation by the weak convergence method. The main difficulty of the
paper is caused by the non-compactness of Sobolev embeddings on unbounded
domains, and the idea of uniform tail-ends estimates is employed to circumvent
the obstacle in order to obtain the tightness of distribution laws of the
stochastic equation and the precompactness of the control equation.
