The aim of this paper is to introduce and analyze a novel fractional chaotic system including quadratic and cubic nonlinearities. We take into account the Caputo derivative for the fractional model and study the stability of the equilibrium points by the fractional Routh–Hurwitz criteria. We also utilize an efficient nonstandard finite difference (NSFD) scheme to implement the new model and investigate its chaotic behavior in both time-domain and phase-plane. According to the obtained results, we find that the new model portrays both chaotic and nonchaotic behaviors for different values of the fractional order, so that the lowest order in which the system remains chaotic is found via the numerical simulations. Afterward, a nonidentical synchronization is applied between the presented model and the fractional Volta equations using an active control technique. The numerical simulations of the master, the slave, and the error dynamics using the NSFD scheme are plotted showing that the synchronization is achieved properly, an outcome which confirms the effectiveness of the proposed active control strategy.

本文的目的是介绍和分析一种新的分数混沌系统，包括二次和三次非线性。我们考虑分数模型的 Caputo 导数，并通过分数 Routh-Hurwitz 准则研究平衡点的稳定性。我们还利用有效的非标准有限差分 (NSFD) 方案来实现新模型并研究其在时域和相平面中的混沌行为。根据获得的结果，我们发现新模型同时描绘了分数阶不同值的混沌和非混沌行为，从而通过数值模拟找到了系统保持混沌的最低阶。之后，使用主动控制技术在所呈现的模型和分数 Volta 方程之间应用了不相同的同步。绘制了使用 NSFD 方案的主机、从机和误差动力学的数值模拟，表明同步已正确实现，这一结果证实了所提出的主动控制策略的有效性。