Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The fractional d'Alembert's formulas   In this paper we develop generalized d'Alembert's formulas for abstract
fractional integro-differential equations and fractional differential equations
on Banach spaces. Some examples are given to illustrate our abstract results,
and the probability interpretation of these fractional d'Alembert's formulas
are also given. Moreover, we also provide d'Alembert's formulas for abstract
fractional telegraph equations.

12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int