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Published in last 1 year |  In last 2 years |  In last 3 years |  All Please wait a minute... For selected: Download citations EndNote Ris BibTeX Toggle thumbnails Select A mathematical analysis: From memristor to fracmemristor 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) Chin. Phys. B, 2022, 31 (6): 060204.   DOI: 10.1088/1674-1056/ac615c Abstract （573）   HTML （4）    PDF （1521KB）（244）       Knowledge map    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. Select Solutions and memory effect of fractional-order chaotic system: A review Shaobo He(贺少波), Huihai Wang(王会海), and Kehui Sun(孙克辉) Chin. Phys. B, 2022, 31 (6): 060501.   DOI: 10.1088/1674-1056/ac43ae Abstract （420）   HTML （10）    PDF （13449KB）（553）       Knowledge map    Fractional calculus is a 300 years topic, which has been introduced to real physics systems modeling and engineering applications. In the last few decades, fractional-order nonlinear chaotic systems have been widely investigated. Firstly, the most used methods to solve fractional-order chaotic systems are reviewed. Characteristics and memory effect in those method are summarized. Then we discuss the memory effect in the fractional-order chaotic systems through the fractional-order calculus and numerical solution algorithms. It shows that the integer-order derivative has full memory effect, while the fractional-order derivative has nonideal memory effect due to the kernel function. Memory loss and short memory are discussed. Finally, applications of the fractional-order chaotic systems regarding the memory effects are investigated. The work summarized in this manuscript provides reference value for the applied scientists and engineering community of fractional-order nonlinear chaotic systems.