Authors: Atanacković, Teodor
Janev, Marko 
Pilipović, Stevan
Affiliations: Mechanics 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Noether’s theorem for variational problems of Herglotz type with real and complex order fractional derivatives
Journal: Acta Mechanica
Volume: 232
Issue: 3
First page: 1131
Last page: 1146
Issue Date: 9-Jan-2021
Rank: ~M22
ISSN: 0001-5970
DOI: 10.1007/s00707-020-02893-3
Abstract: 
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.
Publisher: Springer Link

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