Mathematical and scientific fields of study that are interdisciplinary include chaos theory. chaos theory explains how there is sensitive dependence on initial conditions, meaning that small change in one state of a deterministic nonlinear system can lead to large differences in a later state. The nonvolatile meminductor and memcapacitor models are used to design a nonlinear chaotic oscillating circuit. There is a system of equations derived from chaotic oscillator which is called chaotic oscillator system. The predictor corrector method is presented by using the help of explicit Adams method and implicit Adams method. The predictor corrector method is proposed for solving a chaotic system of differential equations. A new iterative method is proved using characteristics and some fundamental definition of fractional calculus. The new iterative method is used for solving the chaotic system of fractional differential equations. The domain is divided into smaller domains, and an approximative solution for the whole domain can be obtained by solving iteratively. The simulation results are presented. Output chaotic phases are shown in figures. An analysis of the chaotic oscillator system 's stability is conducted.