Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-differentiable variational principles   We develop a calculus of variations for functionals which are defined on a
set of non differentiable curves. We first extend the classical differential
calculus in a quantum calculus, which allows us to define a complex operator,
called the scale derivative, which is the non differentiable analogue of the
classical derivative. We then define the notion of extremals for our
functionals and obtain a characterization in term of a generalized
Euler-Lagrange equation. We finally prove that solutions of the Schr\"odinger
equation can be obtained as extremals of a non differentiable variational
principle, leading to an extended Hamilton's principle of least action for
quantum mechanics. We compare this approach with the scale relativity theory of
Nottale, which assumes a fractal structure of space-time.

12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an