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\begin{document}

\title{A Three Fractional Order Jerk Equation With Anti Periodic Conditions}



\author[1]{Zoubir  DAHMANI}%
\author[1]{Meriem Mansouria  BELHAMITI}%
\author[2]{Mehmet Zeki Sarikaya}%
\affil[1]{Université Abdelhamid Ibn Badis de Mostaganem}%
\affil[2]{Duzce Universitesi}%


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  \date{May 21, 2024}


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\begin{abstract}
We study a new Jerk equation involving three fractional derivatives and
anti periodic conditions. By Banach contraction principle, we present an
existence and uniqueness result for the considered problem. Then, by
applications of Krasnoselskii fixed point theorem, another result for
the existence of at least one solution is established. Also, An
illustrative example is discussed. At the end, an approximation for
Caputo derivaitive is proposed and some chaotic behaviours are discussed
by means of the Runge Kutta 4th order method.%
\end{abstract}%



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