On fractional and distributed orders nonlinear chaotic jerk models and their control

In this paper, we have introduced two versions of the jerk model. These versions are commensurate fractional and distributed orders. They ap-pear in several applications of physics and engineering, e.g., laser physics, damped harmonic oscillators, and secure communications. The sufficient condition for the existence and uniqueness of the solution of commensu-rate fractional-order (CFO) jerk model is studied. We state and prove a theorem to test the dependence of the solutions of the CFO jerk model on initial conditions. The dynamics of the three versions of the jerk model are investigated. Using the largest Lyapunov exponent (LLE), we determine the values of the parameters at which these proposed versions have chaotic solutions. The linear feedback control is used to stabilize the chaotic solu-tions of these versions. Numerical simulations are used to show the chaotic solutions after control.