Fractional stochastic parabolic equations with fractional noise

In this paper, we consider the fractional stochastic parabolic equations driven by fractional noise. We first define the mild solution by the time-fractional Duhamel's principle, then prove the existence and uniqueness of the mild solution by estimating the Fourier transform of the Green function. Furthermore, we explore the Hölder continuity of the mild solution with respect to time and spatial variables.