Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New fractional differential inequalities with their implications to the
  stability analysis of fractional order systems   It is well known that the Leibniz rule for the integer derivative of order
one does not hold for the fractional derivative case when the fractional order
lies between 0 and 1. Thus it poses a great difficulty in the calculation of
fractional derivative of given functions as well as in the analysis of
fractional order systems. In this work, we develop a few fractional
differential inequalities which involve the Caputo fractional derivative of the
product of continuously differentiable functions. We establish some of their
properties and propose a few propositions. We show that these inequalities play
a very essential role in the Lyapunov stability analysis of nonautonomous
fractional order systems.

8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex