Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonlinear stochastic time-fractional diffusion equations on
  $\mathbb{R}$: moments, H\"older regularity and intermittency   We study the nonlinear stochastic time-fractional diffusion equations in the
spatial domain $\mathbb{R}$, driven by multiplicative space-time white noise.
The fractional index $\beta$ varies continuously from $0$ to $2$. The case
$\beta=1$ (resp. $\beta=2$) corresponds to the stochastic heat (resp. wave)
equation. The cases $\beta\in \:]0,1[\:$ and $\beta\in \:]1,2[\:$ are called
{\it slow diffusion equations} and {\it fast diffusion equations},
respectively. Existence and uniqueness of random field solutions with
measure-valued initial data, such as the Dirac delta measure, are established.
Upper bounds on all $p$-th moments $(p\ge 2)$ are obtained, which are expressed
using a kernel function $\mathcal{K}(t,x)$. The second moment is sharp. We
obtain the H\"older continuity of the solution for the slow diffusion equations
when the initial data is a bounded function. We prove the weak intermittency
for both slow and fast diffusion equations. In this study, we introduce a
special function, the {\it two-parameter Mainardi functions}, which are
generalizations of the one-parameter Mainardi functions.

15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph