科创中国

A piecewise memory principle for fractional derivatives

• 摘要：

  In the numerical approximation of fractional order derivatives, the crucial point is to balance the computing complexity and the computing accuracy. We proposed a piecewise memory principle for fractional derivatives, in which the past history is divided into several segments instead of discarded. The piecewise approximation is performed on each segment. Error estimation of piecewise memory principle is analyzed also. Numerical examples show that the contradiction of computing accuracy and complexity is effectively relaxed and the piecewise memory principle is superior to the existing short, variable and equal-weight memory principles. The impacts of the memory length, step size and segment size are also discussed.

• 作者：

  Chunye Gong;为民 包;Jie Liu

• 刊名：

  Fractional Calculus and Applied Analysis

• 在线出版时间：

  2017-8-28