Geodesic
Noether's theorem for Herglotz type variational problems utilizing complex fractional derivatives
Theoretical and applied mechanics, Tome 48 (2021) no. 2

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This is a review article which elaborates the results presented in \cite{Noether_MJ_TMA_SP}, where the 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. The conservation law for the corresponding fractional Euler Lagrange equation is obtained and a sequence of approximations of a fractional Euler--Lagrange equation by systems of integer order equations established and analyzed.
Keywords: Herglotz variational principle, Noether's theorem, fractional derivatives 
@article{TAM_2021_48_2_a3,
     author = {Marko Janev and Teodor M. Atanackovi\'c and Stevan Pilipovi\'c},
     title = {Noether's theorem for {Herglotz} type variational problems utilizing complex fractional derivatives},
     journal = {Theoretical and applied mechanics},
     pages = {127 - 142},
     publisher = {mathdoc},
     volume = {48},
     number = {2},
     year = {2021},
     url = {http://geodesic.mathdoc.fr/item/TAM_2021_48_2_a3/}
}
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Marko Janev; Teodor M. Atanacković; Stevan Pilipović. Noether's theorem for Herglotz type variational problems utilizing complex fractional derivatives. Theoretical and applied mechanics, Tome 48 (2021) no. 2. http://geodesic.mathdoc.fr/item/TAM_2021_48_2_a3/