Holder continuity for stochastic fractional heat equation with colored noise

In this paper, we consider semilinear stochastic fractional heat equation partial derivative u(t)/partial derivative t = - (-Delta)(beta/2)u(t) + sigma(u(t))(eta) over dot. The Gaussian noise (eta) over dot is assumed to be colored in space with covariance of the form E((eta) over dot(t, x)(eta) over dot(s, y)) = delta(0)(t - s)f(alpha)(x - y), where f(alpha) is the Riesz kernel f(alpha)(x) alpha vertical bar x vertical bar(-alpha). We obtain the spatial and temporal Holder continuity of the mild solution. (C) 2017 Elsevier B.V. All rights reserved.