We study a class of stochastic Caputo fractional evolution equations with additive \(Q\) -Wiener noise in a separable Hilbert space. By combining sectorial operator theory with tools from fractional calculus, we employ a Green–Caputo representation for mild solutions. Using this representation, we establish well-posedness, moment estimates, and mean-square stability properties. We also investigate Hyers–Ulam–Rassias stability in the mean-square setting and provide sufficient conditions for this property. In addition, we introduce a Green–Caputo type time-stepping scheme and analyze its strong convergence and discrete stability behavior. Numerical experiments are presented to support the theoretical results.
