Solutions and memory effect of fractional-order chaotic system:A review

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 fractionalorder 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.