The paper investigates the effect of fractional-order parameters on the memristive features such as hysteresis lobe area, the number of pinched points, and their coordinates. In addition, the series-connected fractional-order inductor and capacitor with memristive elements are discussed where the coordinates of the pinched point move away from zero points as $\alpha$ changes. The second-and third-order memristive elements are studied, introducing more than one pinched point with a zero-crossing point in the i - v plane. Four different memristor$⧹$inverse memristors emulators are presented based on several active building blocks. The voltage- and current-controlled emulators are introduced employing the second-generation current conveyor (CCII) and analog multiplier (AM) with generalized impedances. Those emulators are employed to realize the higher-order memristive elements by adding another AM. Switched memristive emulation circuit is also presented based on the extra-x current controlled conveyor (EXCCCII) and two switches. The last introduced memristive emulator consists of one current feedback operational amplifier (CFOA) and two BJT transistors. The introduced circuitry is simulated to validate the presented circuits using PSPICE simulations, and one of them is validated experimentally. Finally, the second-order memristor is employed in Chua’s chaotic oscillator as an application.

该论文研究了分数阶参数对诸如磁滞瓣面积、收缩点数量及其坐标等忆阻特征的影响。此外，讨论了串联的分数阶电感器和带有忆阻元件的电容器，其中收缩点的坐标远离零点为$\alpha$变化。研究了二阶和三阶忆阻元件，在i - v平面中引入了多个具有零交叉点的收缩点。四种不同的忆阻器$⧹$逆忆阻器仿真器基于几个有源构建块提供。电压和电流控制仿真器采用第二代电流传送器 (CCII) 和具有广义阻抗的模拟乘法器 (AM)。这些仿真器用于通过添加另一个 AM 来实现高阶忆阻元件。还提出了基于extra-x电流控制传送器（EXCCCII）和两个开关的开关忆阻仿真电路。最后介绍的忆阻器仿真器由一个电流反馈运算放大器 (CFOA) 和两个 BJT 晶体管组成。引入的电路被模拟以使用 PSPICE 模拟来验证所提出的电路，其中之一是通过实验验证的。最后，在蔡氏混沌振荡器中采用了二阶忆阻器作为应用。