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Chin. Phys. B, 2022, Vol. 31(6): 060204    DOI: 10.1088/1674-1056/ac615c
Special Issue: SPECIAL TOPIC— Interdisciplinary physics: Complex network dynamics and emerging technologies
TOPICAL REVIEW—Interdisciplinary physics: Complex network dynamics and emerging technologies Prev   Next  

A mathematical analysis: From memristor to fracmemristor

Wu-Yang Zhu(朱伍洋)1, Yi-Fei Pu(蒲亦非)1,†, Bo Liu(刘博)1, Bo Yu(余波)2, and Ji-Liu Zhou(周激流)3
1 College of Computer Science, Sichuan University, Chengdu 610065, China;
2 College of Physics and Engineering, Chengdu Normal University, Chengdu 611130, China;
3 Chengdu University of Information Technology, Chengdu 610225, China
Abstract  The memristor is also a basic electronic component, just like resistors, capacitors and inductors. It is a nonlinear device with memory characteristics. In 2008, with HP's announcement of the discovery of the TiO2 memristor, the new memristor system, memory capacitor (memcapacitor) and memory inductor (meminductor) were derived. Fractional-order calculus has the characteristics of non-locality, weak singularity and long term memory which traditional integer-order calculus does not have, and can accurately portray or model real-world problems better than the classic integer-order calculus. In recent years, researchers have extended the modeling method of memristor by fractional calculus, and proposed the fractional-order memristor, but its concept is not unified. This paper reviews the existing memristive elements, including integer-order memristor systems and fractional-order memristor systems. We analyze their similarities and differences, give the derivation process, circuit schematic diagrams, and an outlook on the development direction of fractional-order memristive elements.
Keywords:  fractional calculus      fractional-order memristor      fracmemristor      memristor  
Received:  01 July 2021      Revised:  10 March 2022      Accepted manuscript online:  28 March 2022
PACS:  02.30.Ik (Integrable systems)  
  07.07.Df (Sensors (chemical, optical, electrical, movement, gas, etc.); remote sensing)  
Fund: Project supported in part by the National Natural Science Foundation of China (Grant No. 62171303), China South Industries Group Corporation (Chengdu) Fire Control Technology Center Project (non-secret) (Grant No. HK20-03), and the National Key Research and Development Program Foundation of China (Grant No. 2018YFC0830300).
Corresponding Authors:  Yi-Fei Pu     E-mail:

Cite this article: 

Wu-Yang Zhu(朱伍洋), Yi-Fei Pu(蒲亦非), Bo Liu(刘博), Bo Yu(余波), and Ji-Liu Zhou(周激流) A mathematical analysis: From memristor to fracmemristor 2022 Chin. Phys. B 31 060204

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