Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fractional Differential Equations Involving Caputo Fractional Derivative
  with Mittag-Leffler Non-Singular Kernel: Comparison Principles and
  Applications   In this paper we study linear and nonlinear fractional differential equations
involving the Caputo fractional derivative with Mittag-Leffler non-singular
kernel of order
  $0<\alpha<1.$ We first obtain a new estimate of the fractional derivative of
a function at its extreme points and derive a necessary condition for the
existence of a solution to the linear fractional equation. The obtained
sufficient condition determine the initial condition of the associated
fractional initial value problem. We then derive comparison principles to the
linear fractional equations. We apply these principles to obtain a norm
estimate of solutions to the linear equation and to obtain a uniqueness result
to the nonlinear equation. We also derive a lower and upper bound of solutions
to the nonlinear equation. The applicability of the new results is illustrated
through several examples.

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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
1
The categories of this paper are: cs
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The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph