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.