Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A study on partial dynamic equation on time scales involving derivatives
  of polynomials   Let $\mathbf{P}_b^m(x)$ be a $2m+1-$degree integer-valued polynomial in
$x,b$. Let be a two-dimensional time scale $\Lambda^2 = \mathbb{T}_1 \times
\mathbb{T}_2 = \{t=(x, b) \colon \; x\in\mathbb{T}_1, \; b\in\mathbb{T}_2 \}$.
Let be $\mathbb{T}_1 = \mathbb{T}_2$. In this manuscript we derive and discuss
the following partial dynamic equation on time scales. For every
$t\in\mathbb{T}_1, \; x,b\in \Lambda^2, \; m = const, \; m\in\mathbb{N}$ \[
(t^{2m+1})^{\Delta} = \frac{\partial \mathbf{P}_b^m(x)}{\Delta x} \bigg |_{x =
t, \; b = \sigma(t)} + \frac{\partial \mathbf{P}_b^m(x)}{\Delta b}\bigg |_{x =
t, \; b = t}, \] where $\sigma(t) > t$ is forward jump operator. In addition,
we discuss various derivative operators in context of partial cases of above
equation, we show finite difference, classical derivative, $q-$derivative,
$q-$power derivative on behalf of it.

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The categories of this paper are: eess
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat