A New Definition of Fractional Derivatives Based on Truncated Left-Handed Grünwald-Letnikov Formula with 0 < α < 1 and Median Correction
Author
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-04-12
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Liao, Zhiwu. 2014. A New Definition of Fractional Derivatives Based on Truncated Left-Handed Grünwald-Letnikov Formula with 0 < α < 1 and Median Correction. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-9.
https://search.emarefa.net/detail/BIM-1015046
Modern Language Association (MLA)
Liao, Zhiwu. A New Definition of Fractional Derivatives Based on Truncated Left-Handed Grünwald-Letnikov Formula with 0 < α < 1 and Median Correction. Abstract and Applied Analysis No. 2014 (2014), pp.1-9.
https://search.emarefa.net/detail/BIM-1015046
American Medical Association (AMA)
Liao, Zhiwu. A New Definition of Fractional Derivatives Based on Truncated Left-Handed Grünwald-Letnikov Formula with 0 < α < 1 and Median Correction. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-9.
https://search.emarefa.net/detail/BIM-1015046
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1015046