The existences and asymptotic behavior of solutions to stochastic semilinear anomalous diffusion equations

In this work, we are concerned a class of anomalous diffusion equations with the nonlinearities taking values in Hilbert scales of negative order driven by fractional Brownian motion. By using the resolvent theory, fixed point argument and embeddings of fractional Sobolev spaces we prove the global solvability and give some sufficient conditions to ensure the asymptotic stability of mild solutions in the mean square moment.