Theory Analysis of Left-Handed Grünwald-Letnikov Formula with 0<α<1 to Detect and Locate Singularities

Theory Analysis of Left-Handed Grünwald-Letnikov Formula with 0<α<1 to Detect and Locate Singularities

We study fractional-order derivatives of left-handed Grünwald-Letnikov formula with 0<α<1 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 ar...

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Main Authors: Shaoxiang Hu, Ping Liang
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/157542
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spelling doaj-b58f826ac2df42c68ea7c7df124639232020-11-24T21:43:47ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/157542157542Theory Analysis of Left-Handed Grünwald-Letnikov Formula with 0<α<1 to Detect and Locate SingularitiesShaoxiang Hu0Ping Liang1School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, ChinaNingbo Xingaoyi Co., Ltd., No. 555 Yeshan Road, Yuyao City, Zhejiang 315400, ChinaWe study fractional-order derivatives of left-handed Grünwald-Letnikov formula with 0<α<1 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 0<α<1 can detect and locate four types of ideal singularities correctly, which shows better performance than classical 1-order derivatives in theory.http://dx.doi.org/10.1155/2014/157542
collection DOAJ
language English
format Article
sources DOAJ
author Shaoxiang Hu
Ping Liang
spellingShingle Shaoxiang Hu
Ping Liang
Theory Analysis of Left-Handed Grünwald-Letnikov Formula with 0<α<1 to Detect and Locate Singularities
Abstract and Applied Analysis
author_facet Shaoxiang Hu
Ping Liang
author_sort Shaoxiang Hu
title Theory Analysis of Left-Handed Grünwald-Letnikov Formula with 0<α<1 to Detect and Locate Singularities
title_short Theory Analysis of Left-Handed Grünwald-Letnikov Formula with 0<α<1 to Detect and Locate Singularities
title_full Theory Analysis of Left-Handed Grünwald-Letnikov Formula with 0<α<1 to Detect and Locate Singularities
title_fullStr Theory Analysis of Left-Handed Grünwald-Letnikov Formula with 0<α<1 to Detect and Locate Singularities
title_full_unstemmed Theory Analysis of Left-Handed Grünwald-Letnikov Formula with 0<α<1 to Detect and Locate Singularities
title_sort theory analysis of left-handed grünwald-letnikov formula with 0<α<1 to detect and locate singularities
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2014-01-01
description We study fractional-order derivatives of left-handed Grünwald-Letnikov formula with 0<α<1 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 0<α<1 can detect and locate four types of ideal singularities correctly, which shows better performance than classical 1-order derivatives in theory.
url http://dx.doi.org/10.1155/2014/157542
work_keys_str_mv AT shaoxianghu theoryanalysisoflefthandedgrunwaldletnikovformulawith0a1todetectandlocatesingularities
AT pingliang theoryanalysisoflefthandedgrunwaldletnikovformulawith0a1todetectandlocatesingularities
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