This paper's main objective was to obtain an averaging principle for space-fractional stochastic partial differential equations (SFPDEs) driven by Lévy space-time white noise and fractional Brownian motion (fBm). By using the fixed point theorem, we first obtained the existence and uniqueness of mild solutions for the given equation. Subsequently, given some appropriate conditions, we proved that the solution of the original equation converges to that of the averaged equation as the time scale $ϵ\to 0$. This greatly decreases the complexity since one can focus on the averaged equation rather than the original equation.

In this paper, we investigated the existence and uniqueness of solutions for a class of interactive fuzzy Caputo–Katugampola $F$-correlated fractional differential equations with time delay. First, we gave the definition of the correlated integral and derivative for interactive fuzzy Caputo–Katugampola $F$-correlated systems. Second, we presented an equivalent integral formulation and, under suitable assumptions, established the existence of solutions to fuzzy interactive Caputo–Katugampola $F$-correlated fractional-order differential equations with time delay by applying Schauder's fixed-point theorem. Finally, a numerical example was presented to validate the effectiveness of the proposed approach.