Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algebraic construction of higher order difference approximations for
  fractional derivatives and applications   A generalization of the Gr\"{u}nwald difference approximation for fractional
derivatives in terms of a real sequence and its generating function is
presented. Properties of the generating function are derived for consistency
and order of accuracy for the approximation corresponding to the generator.
Using this generalization, some higher order Gr\"{u}nwald type approximations
are constructed and tested for numerical stability by using steady state
fractional differential problems. These higher order approximations are used in
Crank-Nicolson type numerical schemes to approximate the solution of space
fractional diffusion equations. Stability and convergence of these numerical
schemes are analyzed and are supported by numerical examples.

25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga