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2014 A New Definition of Fractional Derivatives Based on Truncated Left-Handed Grünwald-Letnikov Formula with 0<α<1 and Median Correction
Zhiwu Liao
Abstr. Appl. Anal. 2014(SI64): 1-9 (2014). DOI: 10.1155/2014/914386

Abstract

We propose a new definition of fractional derivatives based on truncated left-handed Grünwald-Letnikov formula with 0<α<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.

Citation

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Zhiwu Liao. "A New Definition of Fractional Derivatives Based on Truncated Left-Handed Grünwald-Letnikov Formula with 0<α<1 and Median Correction." Abstr. Appl. Anal. 2014 (SI64) 1 - 9, 2014. https://doi.org/10.1155/2014/914386

Information

Published: 2014
First available in Project Euclid: 27 February 2015

MathSciNet: MR3198271
Digital Object Identifier: 10.1155/2014/914386

Rights: Copyright © 2014 Hindawi

Vol.2014 • No. SI64 • 2014
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