Zoubir Dahmani, Meriem Mansouria Belhamiti, Mehmet Zeki Sarikaya

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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. Utilizing Krasnoselskii fixed point theorem we prove another existence result governing at least one solution. We provide an illustrative example to claim our established results. At the end, an approximation for Caputo derivative is proposed and some chaotic behaviours are discussed by means of the Runge Kutta 4th order method.


jerk equation, fractional derivatives, anti periodic conditions, fixed point theorem.

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DOI: https://doi.org/10.22190/FUMI210327018D


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