Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: H$\ddot{o}$lder continuity for stochastic fractional heat equation with
  colored noise   In this paper, we consider semilinear stochastic fractional heat equation
$\frac{\partial}{\partial
t}u_{\beta,t}(x)=\triangle^{\alpha/2}u_{\beta,t}(x)+\sigma(u_{\beta,t}(x))\eta_{\beta}$.
The Gaussian noise $\eta_{\beta}$ is assumed to be colored in space with
covariance of the form
$E(\eta_{\beta}(t,x)\eta_{\beta}(s,y))=\delta(t-s)f_{\beta}(x-y)$, where
$f_{\beta}$ is the Riesz kernel $f_{\beta}(x)\propto |x|^{-\beta}$. We obtain
the spatial and temporal H$\ddot{\mbox{o}}$lder continuity of the mild
solution.

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The categories of this paper are: adap-org
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
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The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg