Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Notes on Krasnoselskii-type fixed-point theorems and their application
  to fractional hybrid differential problems   In this paper we prove a new version of Kransoselskii's fixed-point theorem
under a ($\psi, \theta, \varphi$)-weak contraction condition. The theoretical
result is applied to prove the existence of a solution of the following
fractional hybrid differential equation involving
  the Riemann-Liouville differential and integral operators orders of
$0<\alpha<1$ and $\beta>0:$
  \begin{equation}\nonumber
  \left\{\begin{array}{ll} D^{\alpha}[x(t)-f(t, x(t))]=g(t, x(t),
I^{\beta}(x(t))), \,\,\, \text{a.e.} \,\,\, t\in J,\,\, \beta>0,\\
x(t_{0})=x_{0}, \end{array} \right.
  \end{equation}
  where $D^{\alpha}$ is the Riemann-Liouville fractional derivative order of
$\alpha,$ $I^{\beta}$ is Riemann-Liouville fractional integral operator order
of $\beta>0,$ $J=[t_{0}, t_{0}+a],$ for some fixed $t_{0}\in \mathbb{R},$ $a>0$
and the functions $f:J\times \mathbb{R}\rightarrow \mathbb{R}$ and $g:J\times
\mathbb{R}\times \mathbb{R}\rightarrow \mathbb{R}$ satisfy certain conditions.
An example is also furnished to illustrate the hypotheses and the abstract
result of this paper.

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The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
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The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex