Fractional-order circuit is a kind of circuit which contains fractional-order elements. It has been proved that the fractional-order circuit has some characteristics which are hard to be achieved by integer-order circuits, such as higher degree of freedom in circuit design. For integer-order circuits, there are not only non-autonomous circuits, but also autonomous circuits. Since there are many applications of integral-order autonomous circuits in real world, it is also necessary to explore fractional-order autonomous circuits. However, few research focuses on fractional-order autonomous circuits. Therefore, this paper proposes two kinds of fractional-order autonomous circuits based on fractional-order elements with order larger than one. The corresponding mathematical models are also established based on fractional calculus and their characteristics are analyzed based on circuit theory. Finally, circuit simulation are performed to verify the correctness of theoretical analysis.

分数阶电路是一种包含分数阶元素的电路。已经证明，分数阶电路具有某些特征，这些特征是整数阶电路难以实现的，例如电路设计中的较高自由度。对于整数阶电路，不仅有非自治电路，而且还有自治电路。由于积分阶自治电路在现实世界中有许多应用，因此有必要探索分数阶自治电路。但是，很少有研究集中在分数阶自治电路上。因此，本文提出了一种基于阶数大于一的分数阶元素的分数阶自治电路。还基于分数演算建立了相应的数学模型，并基于电路理论分析了它们的特性。最后，进行电路仿真以验证理论分析的正确性。