Hölder continuity for stochastic fractional heat equation with colored noise

In this paper, we consider semilinear stochastic fractional heat equation ∂ut∂t=−(−△)β/2ut+σ(ut)η̇. The Gaussian noise η̇ is assumed to be colored in space with covariance of the form E(η̇(t,x)η̇(s,y))=δ0(t−s)fα(x−y), where fα is the Riesz kernel fα(x)∝∣x∣−α. We obtain the spatial and temporal Hölder continuity of the mild solution.