Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fractional relaxation equations and Brownian crossing probabilities of a
  random boundary   We analyze here different forms of fractional relaxation equations of order
{\nu}\in(0,1) and we derive their solutions both in analytical and in
probabilistic forms. In particular we show that these solutions can be
expressed as crossing probabilities of random boundaries by various types of
stochastic processes, which are all related to the Brownian motion B. In the
special case {\nu}=1/2, the fractional relaxation is proved to coincide with
Pr{sup_{0\leqs\leqt} B(s)<U}, for an exponential boundary U. When we generalize
the distributions of the random boundary, passing from the exponential to the
Gamma density, we obtain more and more complicated fractional equations.

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The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an