Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Definitions of Fractional Sum and Difference on Non-uniform
  Lattices   As is well known, the idea of a fractional sum and difference on uniform
lattice is more current, and gets a lot of development in this field. But the
definitions of fractional sum and fractional difference of $f(z)$ on
non-uniform lattices $x(z)=c_{1}z^{2}+c_{2}z+c_{3}$ or
$x(z)=c_{1}q^{z}+c_{2}q^{-z}+c_{3}$ seem much more difficult and complicated.
In this article, for the first time we propose the definitions of the
fractional sum and fractional difference on non-uniform lattices by two
different ways. The analogue of Euler's Beta formula, Cauchy' Beta formula on
on non-uniform lattices are established, and some fundamental theorems of
fractional calculas, the solution of the generalized Abel equation and
fractional central difference equations on non-uniform lattices are obtained
etc.

32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an