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.
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