This study focuses on establishing the large deviation principle (LDP) for a complex-valued fractional Ginzburg-Landau equation (GLE) influenced by nonlinear noise over the unbounded domain \(\mathbb {R}^d\) . Initially, we prove the well-posedness of the related deterministic control system and obtain the uniform tail estimates for its solutions. Subsequently, we show that the set of controlled solutions exhibits strong convergence when the controls are equipped with the weak topology. By examining the distributional convergence of stochastic solutions as \(\varepsilon \rightarrow 0\) , we rigorously derive the LDP using the weak convergence method. A key challenge arises from the absence of compact Sobolev embeddings in unbounded domains. To address this, uniform tail estimates are introduced, which ensure the tightness of the induced probability measures and the precompactness of control paths. Additionally, the nonlinear drift term \((\mu + i\nu )|X|^{p-2}X\) is handled under the admissible constraint \(|(p-2)\nu | \le 2\mu \sqrt{p-1}\) , guaranteeing uniqueness, continuity, and convergence of solutions. The validity of the results is preserved under the replacement of \((-\Delta )^\alpha \) by the classical Laplace operator. Lastly, numerical experiments are conducted to demonstrate the impact of noise intensity on solution behavior and to provide computational confirmation of the LDP.
