Towards a combined fractional mechanics and quantization

Abstract

A fractional Hamiltonian formalism is introduced for the recent combined fractional calculus of variations. The Hamilton-Jacobi partial differential equation is generalized to be applicable for systems containing combined Caputo fractional derivatives. The obtained results provide tools to carry out the quantization of nonconservative problems through combined fractional canonical equations of Hamilton type. Editorial Note: The authors of this paper (A.B. Malinowska and D.F.M. Torres), together with T. Odzijewicz, have recently received a prestigeous award at the 5th International Symposium "Fractional Differentiation and Applications' 2012" in China, May 14-17, 2012. This is the "Gr̈unwald- Letnikov Award" for Best FDA Student Paper (theory), FDA #084: Green's Theorem for Generalized Fractional Derivatives. See details at http://em.hhu.edu.cn/fda12/Awards.html. © 2012 Diogenes Co., Sofia.