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Abstract and Applied Analysis
Volume 2014, Article ID 157542, 7 pages
http://dx.doi.org/10.1155/2014/157542
Research Article

Theory Analysis of Left-Handed Grünwald-Letnikov Formula with to Detect and Locate Singularities

1School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, China
2Ningbo Xingaoyi Co., Ltd., No. 555 Yeshan Road, Yuyao City, Zhejiang 315400, China

Received 21 January 2014; Accepted 9 March 2014; Published 3 April 2014

Academic Editor: Zhiwu Liao

Copyright © 2014 Shaoxiang Hu and Ping Liang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study fractional-order derivatives of left-handed Grünwald-Letnikov formula with to detect and locate singularities in theory. The widely used four types of ideal singularities are analyzed by deducing their fractional derivative formula. The local extrema of fractional derivatives are used to locate the singularities. Theory analysis indicates that fractional-order derivatives of left-handed Grünwald-Letnikov formula with can detect and locate four types of ideal singularities correctly, which shows better performance than classical 1-order derivatives in theory.