Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fractional Schr\"{o}dinger Equation with singular potentials of
  higher-order   In this paper, the space-fractional Schr\"{o}dinger equations with singular
potentials are studied. Delta-like or even higher-order singularities are
allowed. By using the regularising techniques, we introduce a family of
'weakened' solutions, calling them very weak solutions. The existence,
uniqueness and consistency results are proved in an appropriate sense.
Numerical simulations are done, and a particle accumulating effect is observed
in the singular cases. From the mathematical point of view, a "splitting of the
strong singularity" phenomena is also observed.

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The categories of this paper are: cs
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph