Currently, there are mainly three semi-analytical solution algorithms for fractional-order chaotic systems, and they are multistep Adomian decomposition algorithm, multistep differential transform method and multistep Homotopy analysis algorithm. Obviously, they are different from the Adams-Bashforth-Moulton (ABM) solution algorithm. Usually, the semi-analytical solution algorithms are represented as x(n+1)=F(x(n)), while ABM solution is given by x(n+1)=G(x(n), x(n-1), …, x(1), x(0)). Therefore, ABM is calculated based on the whole memory data, while solutionsof the semi-analytical solution algorithms just based on the previous data. Currently, we have some articles on dynamics of fractional-order chaotic systems. It shows that those semi-analytical solution algorithms are effective and can be realized in the digital processors like DSP. However, the definitions of fractional derivative are memorability. Thus I really want to know how to exact understand memory effect in those three semi-analytical solution algorithms
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