Open AccessNoether’s theorem for Herglotz type variational problems utilizing complex fractional derivatives
Author(s) -
Marko Janev,
Teodor M. Atanacković,
Stevan Pilipović
Publication year - 2021
Publication title -
theoretical and applied mechanics/theoretical and applied mechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.279
H-Index - 6
eISSN - 2406-0925
pISSN - 1450-5584
DOI - 10.2298/tam210913011j
Subject(s) - noether's theorem , mathematics , homogeneous space , conservation law , type (biology) , action (physics) , fractional calculus , variational principle , order (exchange) , euler's formula , integer (computer science) , symmetry (geometry) , lagrangian , mathematical analysis , physics , quantum mechanics , ecology , geometry , finance , computer science , economics , biology , programming language
This is a review article which elaborates the results presented in [1], 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.