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In this article, we consider the stochastic fractional diffusion equation ∂β+ ν2 −Δα∕2u(t,x)=λI0+γu(t,x)W˙(t,x),t>0,x∈R, where α>0, β∈(0,2], γ≥0, λ≠0, ν>0, and W˙ is a Gaussian noise which is white or fractional in time and rough in space. We prove the existence and uniqueness of the solution in the Itô-Skorohod sense and obtain the lower and upper bounds for the p-th moment. The Hölder regularity of the solution is also studied.
Guo et al. (Wed,) studied this question.