Variational Problems with Partial Fractional Derivative: Optimal Conditions and Noether’s Theorem
In this paper, the necessary and sufficient conditions of optimality for variational problems with Caputo partial fractional derivative are established. Fractional Euler-Lagrange equations are obtained. The Legendre condition and Noether’s theorem are also presented.
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2018/4197673 |
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| _version_ | 1849434716377186304 |
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| author | Jun Jiang Yuqiang Feng Shougui Li |
| author_facet | Jun Jiang Yuqiang Feng Shougui Li |
| author_sort | Jun Jiang |
| collection | DOAJ |
| description | In this paper, the necessary and sufficient conditions of optimality for variational problems with Caputo partial fractional derivative are established. Fractional Euler-Lagrange equations are obtained. The Legendre condition and Noether’s theorem are also presented. |
| format | Article |
| id | doaj-art-e37e674ad21a4ef084de072c746a8550 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-e37e674ad21a4ef084de072c746a85502025-08-20T03:26:33ZengWileyJournal of Function Spaces2314-88962314-88882018-01-01201810.1155/2018/41976734197673Variational Problems with Partial Fractional Derivative: Optimal Conditions and Noether’s TheoremJun Jiang0Yuqiang Feng1Shougui Li2School of Science, Wuhan University of Science and Technology, Wuhan 430065, Hubei, ChinaSchool of Science, Wuhan University of Science and Technology, Wuhan 430065, Hubei, ChinaSchool of Science, Wuhan University of Science and Technology, Wuhan 430065, Hubei, ChinaIn this paper, the necessary and sufficient conditions of optimality for variational problems with Caputo partial fractional derivative are established. Fractional Euler-Lagrange equations are obtained. The Legendre condition and Noether’s theorem are also presented.http://dx.doi.org/10.1155/2018/4197673 |
| spellingShingle | Jun Jiang Yuqiang Feng Shougui Li Variational Problems with Partial Fractional Derivative: Optimal Conditions and Noether’s Theorem Journal of Function Spaces |
| title | Variational Problems with Partial Fractional Derivative: Optimal Conditions and Noether’s Theorem |
| title_full | Variational Problems with Partial Fractional Derivative: Optimal Conditions and Noether’s Theorem |
| title_fullStr | Variational Problems with Partial Fractional Derivative: Optimal Conditions and Noether’s Theorem |
| title_full_unstemmed | Variational Problems with Partial Fractional Derivative: Optimal Conditions and Noether’s Theorem |
| title_short | Variational Problems with Partial Fractional Derivative: Optimal Conditions and Noether’s Theorem |
| title_sort | variational problems with partial fractional derivative optimal conditions and noether s theorem |
| url | http://dx.doi.org/10.1155/2018/4197673 |
| work_keys_str_mv | AT junjiang variationalproblemswithpartialfractionalderivativeoptimalconditionsandnoetherstheorem AT yuqiangfeng variationalproblemswithpartialfractionalderivativeoptimalconditionsandnoetherstheorem AT shouguili variationalproblemswithpartialfractionalderivativeoptimalconditionsandnoetherstheorem |