Noether’s theorem for variational problems of Herglotz type with real and complex order fractional derivatives

Autor:	Stevan Pilipović, Teodor M. Atanackovic, Marko Janev
Jazyk:	angličtina
Rok vydání:	2021
Předmět:	Sequence Conservation law Mechanical Engineering Computational Mechanics Action (physics) Fractional calculus symbols.namesake Integer Variational principle Homogeneous space symbols Applied mathematics Noether's theorem Mathematics
Zdroj:	Acta Mechanica. 232(3):1131-1146
ISSN:	0001-5970
DOI:	10.1007/s00707-020-02893-3
Popis:	A variational principle of Herglotz type with a Lagrangian that depends on fractional derivatives of both real and complex orders is formulated, and the invariance of this principle under the action of a local group of symmetries is determined. By the Noether theorem the conservation law for the corresponding fractional Euler–Lagrange equation is obtained. A sequence of approximations of a fractional Euler–Lagrange equation by systems of integer order equations is used for the construction of a sequence of conservation laws which, with certain assumptions, weakly converge to the one for the basic Herglotz variational principle. Results are illustrated by two examples. © 2021, Springer-Verlag GmbH Austria, part of Springer Nature.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bf26370914bcc8a9d9a5557ddcbf092b https://doi.org/10.1007/s00707-020-02893-3 Zobrazit plný text záznamu Plný text ve formátu PDF Plný text ve formátu HTML
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