Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Calculus of Variations on Time Scales and Discrete Fractional Calculus   We study problems of the calculus of variations and optimal control within
the framework of time scales. Specifically, we obtain Euler-Lagrange type
equations for both Lagrangians depending on higher order delta derivatives and
isoperimetric problems. We also develop some direct methods to solve certain
classes of variational problems via dynamic inequalities. In the last chapter
we introduce fractional difference operators and propose a new discrete-time
fractional calculus of variations. Corresponding Euler-Lagrange and Legendre
necessary optimality conditions are derived and some illustrative examples
provided.

20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th