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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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/157542 |
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| _version_ | 1832562555273347072 |
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| author | Shaoxiang Hu Ping Liang |
| author_facet | Shaoxiang Hu Ping Liang |
| author_sort | Shaoxiang Hu |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-b58f826ac2df42c68ea7c7df12463923 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-b58f826ac2df42c68ea7c7df124639232025-02-03T01:22:23ZengWileyAbstract 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 |
| 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 |
| title | 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_short | Theory Analysis of Left-Handed Grünwald-Letnikov Formula with 0<α<1 to Detect and Locate Singularities |
| title_sort | theory analysis of left handed grunwald letnikov formula with 0 α 1 to detect and locate singularities |
| url | http://dx.doi.org/10.1155/2014/157542 |
| work_keys_str_mv | AT shaoxianghu theoryanalysisoflefthandedgrunwaldletnikovformulawith0a1todetectandlocatesingularities AT pingliang theoryanalysisoflefthandedgrunwaldletnikovformulawith0a1todetectandlocatesingularities |