Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Integro-Differential Equation of the Fractional Form: Cauchy Problem
  and Solution   We solve the Cauchy problem defined by the fractional partial differential
equation $[\partial_{tt}-\kappa\mathbb{D}]u=0$, with $\mathbb{D}$ the
pseudo-differential Riesz operator of first order, and the initial conditions
$u(x,0)=\mu(\sqrt{\pi}x_0)^{-1}e^{-(x/x_0)^2}$, $u_t(x,0)=0$. The solution of
the Cauchy problem resulting from the substitution of the Gaussian pulse
$u(x,0)$ by the Dirac delta distribution $\varphi(x)=\mu\delta(x)$ is obtained
as corollary.

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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc
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The categories of this paper are: econ
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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-th
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The categories of this paper are: funct-an
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The categories of this paper are: nlin
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The categories of this paper are: supr-con
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex