Abstract
In this paper, we research Noether’s theorems of fractional generalized Birkhoffian systems in terms of classical and combined Caputo derivatives. First, the generalized Pfaff–Birkhoff principle and Birkhoff’s equations with classical and combined Caputo derivatives are given. Then, in the case of without and with transforming time, respectively, we obtain two kinds of Noether symmetry and their conserved quantities by the method of time re-parameterization. Finally, by taking case of generalized Birkhoffian systems, we study the relationship between Noether symmetry and Mei symmetry. It is concluded that the generalized Birkhoff equations, Noether identity and Noether conserved quantity obtained by using the generalized Pfaff–Birkhoff principle based on the action functional with dynamical functions after infinitesimal transformation are completely consistent with the criterion equation, structural equation and Mei conserved quantity of the fractional generalized Birkhoffian system, respectively.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.