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- Title
Fractional Noether's theorem with classical and Caputo derivatives: constants of motion for non-conservative systems.
- Authors
Frederico, G.; Lazo, M.
- Abstract
Since the seminal work of Emmy Noether, it is well know that all conservations laws in physics, e.g., conservation of energy or conservation of momentum, are directly related to the invariance of the action under a family of transformations. However, the classical Noether's theorem cannot yield information about constants of motion for non-conservative systems since it is not possible to formulate physically meaningful Lagrangians for this kind of systems in classical calculus of variation. On the other hand, in recent years the fractional calculus of variation within Lagrangians depending on fractional derivatives has emerged as an elegant alternative to study non-conservative systems. In the present work, we obtained a generalization of the Noether's theorem for Lagrangians depending on mixed classical and Caputo derivatives that can be used to obtain constants of motion for dissipative systems. In addition, we also obtained Noether's conditions for the fractional optimal control problem.
- Subjects
NOETHER'S theorem; CAPUTO fractional derivatives; FRACTIONAL calculus; OPTIMAL control theory; MOMENTUM wave function
- Publication
Nonlinear Dynamics, 2016, Vol 85, Issue 2, p839
- ISSN
0924-090X
- Publication type
Article
- DOI
10.1007/s11071-016-2727-z