Fractional calculus (FC) is widely used in many interdisciplinary branches of science due to its effectiveness in describing and investigating complicated phenomena. In this work, nonlinear dynamics for a new physical model using nonlocal fractional differential operator with singular kernel is introduced. New Routh-Hurwitz stability conditions are derived for the fractional case as the order lies in [0,2). The new and basic Routh-Hurwitz conditions are applied to the commensurate case. The local stability of the incommensurate orders is also discussed. A sufficient condition is used to prove that the solution of the proposed system exists and is unique in a specific region. Conditions for the approximating periodic solution in this model via Hopf bifurcation theory are discussed. Chaotic dynamics are found in the commensurate system for a wide range of fractional orders. The Lyapunov exponents and Lyapunov spectrum of the model are provided. Suppressing chaos in this system is also achieved via two different methods.

小数演算（FC）因其在描述和研究复杂现象方面的有效性而被广泛用于科学的许多跨学科分支。在这项工作中，引入了使用具有奇异核的非局部分数阶微分算子的新物理模型的非线性动力学。对于小数情况，导出了新的Routh-Hurwitz稳定性条件，其阶数为[0,2）。新的和基本的劳斯·赫维兹条件适用于相应的情况。还讨论了不相称订单的局部稳定性。使用足够的条件来证明提出的系统的解决方案存在并且在特定区域中是唯一的。通过Hopf分叉理论讨论了该模型中近似周期解的条件。在相称系统中发现了广泛的分数阶混沌动力学。提供了模型的Lyapunov指数和Lyapunov谱。还可以通过两种不同的方法来抑制该系统中的混乱。