Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Left fractional Sobolev space via Riemann$-$Liouville derivatives on
  time scales and its application to a fractional boundary value problem on
  time scales   We first prove the equivalence of two definitions of Riemann-Liouville
fractional integral on time scales, then by the concept of fractional
derivative of Riemann-Liouville on time scales, we introduce fractional Sobolev
spaces, characterize them, define weak fractional derivatives, and show that
they coincide with the Riemann-Liouville ones on time scales. Next, we prove
equivalence of some norms in the introduced spaces and derive their
completeness, reflexivity, separability and some imbeddings. Finally, as an
application, by constructing an appropriate variational setting, using the
mountain pass theorem and the genus properties, the existence of weak solutions
for a class of Kirchhoff-type fractional p-Laplacian systems on time scales
with boundary condition is studied, and three results of the existence of weak
solutions for this problem is obtained.

18
The categories of this paper are: econ
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio