Averaging principle for space-fractional stochastic partial differential equations driven by Lévy white noise and fractional Brownian motion

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.