Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Necessary and sufficient conditions for the fractional calculus of
  variations with Caputo derivatives   We prove optimality conditions for different variational functionals
containing left and right Caputo fractional derivatives. A sufficient condition
of minimization under an appropriate convexity assumption is given. An
Euler-Lagrange equation for functionals where the lower and upper bounds of the
integral are distinct of the bounds of the Caputo derivative is also proved.
Then, the fractional isoperimetric problem is formulated with an integral
constraint also containing Caputo derivatives. Normal and abnormal extremals
are considered.

22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
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The categories of this paper are: stat
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ