A New Definition of Fractional Derivatives Based on Truncated Left-Handed Grunwald-Letnikov Formula with 0 < alpha < 1 and Median Correction

作者：Liao Zhiwu^*

来源：Abstract and Applied Analysis, 2014, 2014: 914386.

DOI：10.1155/2014/914386

We propose a new definition of fractional derivatives based on truncated left-handed Gruunwald-Letnikov formula with 0 < alpha < 1 and median correction. Analyzing the difficulties to choose the fractional orders and unsatisfied processing results in signal processing using fractional-order partial differential equations and related methods; we think that the nonzero values of the truncated fractional order derivatives in the smooth regions are major causes for these situations. In order to resolve the problem, the absolute values of truncated parts of the G-L formula are estimated by the median of signal values of the remainder parts, and then the truncated G-L formula is modified by replacing each of the original signal value to the differences of the signal value and the median. Since the sum of the coefficients of the G-L formula is zero, the median correction can reduce the truncated errors greatly to proximate G-L formula better. We also present some simulation results and experiments to support our theory analysis.

• 出版日期2014
• 单位四川师范大学