Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A derivative concept with respect to an arbitrary kernel and
  applications to fractional calculus   In this paper, we propose a new concept of derivative with respect to an
arbitrary kernel-function. Several properties related to this new operator,
like inversion rules, integration by parts, etc. are studied. In particular, we
introduce the notion of conjugate kernels, which will be useful to guaranty
that the proposed derivative operator admits a right inverse. The proposed
concept includes as special cases Riemann-Liouville fractional derivatives,
Hadamard fractional derivatives, and many other fractional operators. Moreover,
using our concept, new fractional operators involving certain special functions
are introduced, and some of their properties are studied. Finally, an existence
result for a boundary value problem involving the introduced derivative
operator is proved.

6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex