Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convolution series and the generalized convolution Taylor formula   In this paper, we deal with the convolution series that are a far reaching
generalization of the conventional power series and the power series with the
fractional exponents including the Mittag-Leffler type functions. Special
attention is given to the most interesting case of the convolution series
generated by the Sonine kernels. In this paper, we first formulate and prove
the second fundamental theorem for the general fractional integrals and the
$n$-fold general sequential fractional derivatives of both the
Riemann-Liouville and the Caputo types. These results are then employed for
derivation of two different forms of a generalized convolution Taylor formula
for representation of a function as a convolution polynomial with a remainder
in form of a composition of the $n$-fold general fractional integral and the
$n$-fold general sequential fractional derivative of the Riemann-Liouville and
the Caputo types, respectively. We also discuss the generalized Taylor series
in form of convolution series and deduce the formulas for its coefficients in
terms of the $n$-fold general sequential fractional derivatives.

1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph