Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Towards Fractional Gradient Elasticity   An extension of gradient elasticity through the inclusion of spatial
derivatives of fractional order to describe power-law type of non-locality is
discussed. Two phenomenological possibilities are explored. The first is based
on the Caputo fractional derivatives in one-dimension. The second involves the
Riesz fractional derivative in three-dimensions. Explicit solutions of the
corresponding fractional differential equations are obtained in both cases. In
the first case it is shown that stress equilibrium in a Caputo elastic bar
requires the existence of a non-zero internal body force to equilibrate it. In
the second case, it is shown that in a Riesz type gradient elastic continuum
under the action of a point load, the displacement may or may not be singular
depending on the order of the fractional derivative assumed.

18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
2
The categories of this paper are: math
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex