Boundary-driven stochastic fractional CGL equations with non-Gaussian noise on multidimensional domains

This paper investigates a class of stochastic nonlinear fractional partial differential equations of complex Ginzburg-Landau (CGL) type posed on the multidimensional positive orthant. The model incorporates both interior multiplicative noise and Robin-type stochastic boundary forcing, acting independently along each coordinate hyperplane. The governing equation includes a vectorial Caputo-type fractional Laplacian of order (32, 2), a nonlinear term of the cubic type and non-Gaussian noise introduced via the modulus of Brownian motions convolved with deterministic kernels. We focus on the formulation and analysis of mild solutions under minimal smoothness assumptions. The main analytical challenges stem from the nonlocal nature of fractional diffusion, the loss of martingale structure due to non-centered boundary noise, and the intricate coupling induced by Robin-type conditions in multiple spatial dimensions. We develop a novel framework combining infinite-dimensional Itô calculus, Laplace-transform methods, and weighted fractional Sobolev estimates. Our contributions include the construction of a well-posed mild solution framework, the derivation of probabilistic a priori bounds, and second moment estimates. We also characterize the long-time behavior of solutions, identifying decay rates and stochastic regularization phenomena driven by the fractional Laplacian. The novelty of this work lies in the synthesis of fractional diffusion, nonlinear complex dynamics, and non-Gaussian boundary noise—a setting that remains largely unexplored. Unlike previous studies restricted to Gaussian interior noise, our approach captures realistic dynamics involving delayed boundary responses and spatially distributed stochastic inputs. These results offer new insights into the behavior of boundary-driven fractional SPDEs and provide a foundation for future work in stochastic modeling of anomalous transport and interface phenomena.