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\title[Fractional order differential inclusions]
{\large Fractional order differential inclusions \\ on an unbounded domain with infinite delay}

\author[M. Helal]{MOHAMED HELAL}


\begin{abstract}
In this paper, we provide sufficient conditions for the existence of solutions to initial
value problems, for partial hyperbolic differential inclusions of fractional order involving
Caputo fractional derivative with infinite delay by applying the nonlinear alternative of
Frigon type for multivalued admissible contraction in Fr\'echet spaces.
\end{abstract}

\begin{amssubject}
26A33, 34K30, 34K37, 35R11.
\end{amssubject}

\begin{keyword}
Partial functional differential inclusion, fractional order, solution, left-sided mixed
Riemann-Liouville integral, Caputo fractional-order derivative,
infinite delay, Fr\'echet space, fixed point.
\end{keyword}

\thanks{The author is grateful to the referees for their helpful comments and suggestions.}

\maketitle

\let\thefootnote\relax\footnote{ \ }\hspace{-5mm}\let\thefootnote\relax\footnote{\hspace{-13pt}DOI: 10.24193/mathcluj.2020.2.06}



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\vspace{10pt}

\hspace{-4mm}{\small{Received August 1, 2019}}\\
\hspace{-4mm}{\small{Accepted October 16, 2019}}

% ADDRESS
\vspace{-25.3pt}
\ \hfill
\begin{tabular}{c}
{\small\em Mustapha Stambouli University of Mascara}\\
{\small\em Science and Technology Faculty}\\
{\small\em Djillali Liabes University of Sidi Bel-Abb\`es}\\
{\small\em Laboratory of Mathematics}\\
{\small\em Algeria}\\
{\small\em E-mail: {\tt helalmohamed@univ-mascara.dz}}
\end{tabular}

\end{document} 
