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\begin{document}

\title{Analyses of solutions of Riemann-Liouville fractional oscillatory
differential equations with pure delay}



\author[1]{Zhenbin  Fan}%
\author[1]{Renjie Pan}%
\affil[1]{Yangzhou University College of Mathematical Sciences}%


\vspace{-1em}



  
  \date{May 25, 2024}


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\begin{abstract}
This paper firstly finishes off the exact solutions of Riemann-Liouville
fractional differential time-delay oscillatory system of order
\selectlanguage{greek}\emph{ρ}\selectlanguage{english}[?]\selectlanguage{english}(1 \emph{,}2) by using two newly defined delayed perturbations
of Mittag-Leffler matrix functions and constant variation method. In the
light of the exact solutions, we explore the finite time stability of
the nonhomogeneous fractional oscillatory differential equations with
pure delay. Ultimately, an example is cited to verify the rationality of
the results. Through our method, the public problems left by Mahmudov in
2022 were partially solved.%
\end{abstract}%



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