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H$\ddot{o}$lder continuity for stochastic fractional heat equation with colored noise

In this paper, we consider semilinear stochastic fractional heat equation $\frac{\partial}{\partial t}u_{β,t}(x)=\triangle^{α/2}u_{β,t}(x)+σ(u_{β,t}(x))η_β$. The Gaussian noise $η_β$ is assumed to be colored in space with covariance of the form $E(η_β(t,x)η_β(s,y))=δ(t-s)f_β(x-y)$, where $f_β$ is the Riesz kernel $f_β(x)\propto |x|^{-β}$. We obtain the spatial and temporal H$\ddot{\mbox{o}}$lder continuity of the mild solution.