Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Leibniz rule and Laplace transform for fractional derivatives   Taylor series is a useful mathematical tool when describing and constructing
a function. With the series representation, some properties of fractional
calculus can be revealed clearly. This paper investigates two typical
applications: Lebiniz rule and Laplace transform. It is analytically shown that
the commonly used Leibniz rule cannot be applied for Caputo derivative.
Similarly, the well-known Laplace transform of Riemann-Liouville derivative is
doubtful for n-th continuously differentiable function. By the aid of this
series representation, the exact formula of Caputo Leibniz rule and the
explanation of Riemann-Liouville Laplace transform are presented. Finally,
three illustrative examples are revisited to confirm the obtained results.

20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio