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
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

Show full item record


checked on Jun 15, 2024

Page view(s)

checked on May 9, 2024

Google ScholarTM




Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.