Bertrand’s theorem and virial theorem in fractional classical mechanics
School of Information and Mathematics, Yangtze University, Jingzhou, 434023, Hubei, China
2 Department of Physics, East China Normal University, 200241, Shanghai, China
* e-mail: firstname.lastname@example.org
Accepted: 29 June 2017
Published online: 11 September 2017
Fractional classical mechanics is the classical counterpart of fractional quantum mechanics. The central force problem in this theory is investigated. Bertrand's theorem is generalized, and virial theorem is revisited, both in three spatial dimensions. In order to produce stable, closed, non-circular orbits, the inverse-square law and the Hooke's law should be modified in fractional classical mechanics.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, 2017