Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Variational formulation of problems involving fractional order
  differential operators   In this work, we consider boundary value problems involving Caputo and
Riemann-Liouville fractional derivatives of order $\alpha\in(1,2)$ on the unit
interval $(0,1)$. These fractional derivatives lead to non-symmetric boundary
value problems, which are investigated from a variational point of view. The
variational problem for the Riemann-Liouville case is coercive on the space
$H_0^{\alpha/2}(0,1)$ but the solutions are less regular, whereas that for the
Caputo case involves different test and trial spaces. The numerical analysis of
these problems requires the so-called shift theorems which show that the
solutions of the variational problem are more regular. The regularity pickup
enables one to establish convergence rates of the finite element
approximations. Finally, numerical results are presented to illustrate the
error estimates.

15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ