Random attractors for fractional stochastic reaction–diffusion systems with fractional Brownian motion

Abstract

Fractional stochastic reaction–diffusion systems involving fractional Brownian motion (fBm) provide a comprehensive modeling framework for studying complex physical and biological phenomena. In this study, we investigate the dynamic behavior of solutions to fractional stochastic reaction–diffusion systems with fBm defined on Rn. Firstly, we establish the existence and uniqueness of solutions to the fractional stochastic reaction–diffusion systems with fBm. We also obtain uniform estimates for the solutions on average. Furthermore, we construct a mean random dynamical system based on the derived solutions. Finally, we prove the existence and uniqueness of weak pullback mean random attractors. The results of our investigation contribute to a deeper understanding of the complexities involved in reaction–diffusion processes, specifically considering the effect of fBm with long-range dependence and self-similarity properties. Additionally, our findings have broader applications, particularly in areas such as analyzing the dynamic behavior of complex systems and biological models.