Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a Fractional Oscillator Equation with Natural Boundary Conditions   We prove existence of solutions for a nonlinear fractional oscillator
equation with both left Riemann-Liouville and right Caputo fractional
derivatives subject to natural boundary conditions. The proof is based on a
transformation of the problem into an equivalent lower order fractional
boundary value problem followed by the use of an upper and lower solutions
method. To succeed with such approach, we first prove a result on the
monotonicity of the right Caputo derivative.

17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph