The operation of memristive, meminductive and memcapacitive circuit components depend on their history of devices, i.e. they are memory dependent. This paper proposes new fractional-order (FO) models of four such circuits since FO derivative is calculated using the past history of time and helps in understanding the memory-dependent dynamics of these memory devices better as compared to the integral derivative. Interestingly, these fractional-order memristive, meminductive and memcapacitive systems (FOMMMSs) display a myriad of dynamics such as ranging from coexisting to hidden attractors, chaotic to hyperchaotic attractors, periodic orbits to stable foci, bursting oscillations transitioning from chaos to periodic states and vice versa, offset boosting phenomenon, and a varied nature of infinite equilibria. The proposed fractional-order systems can have a number of applications such as in oscillator circuits, and secure communication due to the increased randomness of hidden multistability. The theoretical analyses of existence of multistability and hidden attractors in the proposed FOMMMSs comply with that of the numerical simulation and circuit implementation results.

忆阻、忆阻和忆容电路元件的操作取决于它们的器件历史，即它们依赖于存储器。本文提出了四个此类电路的新分数阶 (FO) 模型，因为 FO 导数是使用过去的时间历史计算的，并且与积分导数相比，有助于更好地理解这些存储设备的内存相关动态。有趣的是，这些分数阶忆阻、忆阻和记忆电容系统 (FOMMMS) 显示出无数的动力学，例如从共存到隐藏吸引子、从混沌到超混沌吸引子、从周期轨道到稳定焦点、从混沌状态过渡到周期状态的爆发振荡等等。反之亦然，抵消促进现象，以及无限平衡的变化性质。所提出的分数阶系统可以有许多应用，例如在振荡器电路中，以及由于隐藏的多稳定性增加的随机性而导致的安全通信。所提出的 FOMMMS 中存在多稳态和隐藏吸引子的理论分析与数值模拟和电路实现结果一致。