%A Shaobo He(贺少波), Huihai Wang(王会海), and Kehui Sun(孙克辉) %T Solutions and memory effect of fractional-order chaotic system: A review %0 Journal Article %D 2022 %J Chin. Phys. B %R 10.1088/1674-1056/ac43ae %P 60501-060501 %V 31 %N 6 %U {https://cpb.iphy.ac.cn/CN/abstract/article_124739.shtml} %8 2022-05-17 %X 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.