Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Maximum principles, extension problem and inversion for nonlocal
  one-sided equations   We study one-sided nonlocal equations of the form
$$\int_{x_0}^\infty\frac{u(x)-u(x_0)}{(x-x_0)^{1+\alpha}} dx=f(x_0),$$ on the
real line. Notice that to compute this nonlocal operator of order $0<\alpha<1$
at a point $x_0$ we need to know the values of $u(x)$ to the right of $x_0$,
that is, for $x\geq x_0$. We show that the operator above corresponds to a
fractional power of a one-sided first order derivative. Maximum principles and
a characterization with an extension problem in the spirit of
Caffarelli--Silvestre and Stinga--Torrea are proved. It is also shown that
these fractional equations can be solved in the general setting of weighted
one-sided spaces. In this regard we present suitable inversion results. Along
the way we are able to unify and clarify several notions of fractional
derivatives found in the literature.

16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
9
The categories of this paper are: nlin