2016/03/06 by Gastão S. F. Frederico, Frederico, Gastão S. F., Matheus J. Lazo +1
Mathematics · Physics and Astronomy · #Experimental and Theoretical Physics Studies #FOS: Mathematics #FOS: Physical sciences #Fractional Differential Equations Solutions #Mathematical Physics (math-ph) #Numerical methods for differential equations #Optimization and Control (math.OC) #math-ph #math.MP #math.OC
paper · pdf · doi:10.48550/arxiv.1603.01822
accepted for publication in Nonlinear Dynamics. arXiv admin note: text overlap with arXiv:1209.1330
arxiv created 2016/03/06 · openalex publication_date 2016/03/06 · arxiv updated 2016/03/16 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28
Since the seminal work of Emmy Noether it is well know that all conservations laws in physics, \textrme.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 can not yields informations about constants of motion for non-conservative systems since it is not possible to formulate physically meaningful Lagragians 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.