Advanced Methods in the Fractional Calculus of Variations

This brief presents a general unifying perspective on the fractional calculus. It brings together results of several recent approaches in generalizing the least action principle and the Euler–Lagrange equations to include fractional derivatives. The dependence of Lagrangians on generalized fraction...

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Những tác giả chính:	Malinowska, Agnieszka B, Odzijewicz, Tatiana, Torres, Delfim F.M.
Định dạng:	Sách
Ngôn ngữ:	English
Được phát hành:	Springer 2015
Những chủ đề:	Fractional calculus Calculus of variations Calculus Mathematics
Truy cập trực tuyến:	https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/58682
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spelling	oai:scholar.dlu.edu.vn:DLU123456789-586822023-11-11T06:18:03Z Advanced Methods in the Fractional Calculus of Variations Malinowska, Agnieszka B Odzijewicz, Tatiana Torres, Delfim F.M. Fractional calculus Calculus of variations Calculus Mathematics This brief presents a general unifying perspective on the fractional calculus. It brings together results of several recent approaches in generalizing the least action principle and the Euler–Lagrange equations to include fractional derivatives. The dependence of Lagrangians on generalized fractional operators as well as on classical derivatives is considered along with still more general problems in which integer-order integrals are replaced by fractional integrals. General theorems are obtained for several types of variational problems for which recent results developed in the literature can be obtained as special cases. In particular, the authors offer necessary optimality conditions of Euler–Lagrange type for the fundamental and isoperimetric problems, transversality conditions, and Noether symmetry theorems. 2015-10-02T01:19:43Z 2015-10-02T01:19:43Z 2015 Book 978-3-319-14756-7 https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/58682 en application/pdf Springer
institution	Thư viện Trường Đại học Đà Lạt
collection	Thư viện số
language	English
topic	Fractional calculus Calculus of variations Calculus Mathematics
spellingShingle	Fractional calculus Calculus of variations Calculus Mathematics Malinowska, Agnieszka B Odzijewicz, Tatiana Torres, Delfim F.M. Advanced Methods in the Fractional Calculus of Variations
description	This brief presents a general unifying perspective on the fractional calculus. It brings together results of several recent approaches in generalizing the least action principle and the Euler–Lagrange equations to include fractional derivatives. The dependence of Lagrangians on generalized fractional operators as well as on classical derivatives is considered along with still more general problems in which integer-order integrals are replaced by fractional integrals. General theorems are obtained for several types of variational problems for which recent results developed in the literature can be obtained as special cases. In particular, the authors offer necessary optimality conditions of Euler–Lagrange type for the fundamental and isoperimetric problems, transversality conditions, and Noether symmetry theorems.
format	Book
author	Malinowska, Agnieszka B Odzijewicz, Tatiana Torres, Delfim F.M.
author_facet	Malinowska, Agnieszka B Odzijewicz, Tatiana Torres, Delfim F.M.
author_sort	Malinowska, Agnieszka B
title	Advanced Methods in the Fractional Calculus of Variations
title_short	Advanced Methods in the Fractional Calculus of Variations
title_full	Advanced Methods in the Fractional Calculus of Variations
title_fullStr	Advanced Methods in the Fractional Calculus of Variations
title_full_unstemmed	Advanced Methods in the Fractional Calculus of Variations
title_sort	advanced methods in the fractional calculus of variations
publisher	Springer
publishDate	2015
url	https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/58682
_version_	1782532460933808128

Advanced Methods in the Fractional Calculus of Variations

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