Towards a combined fractional mechanics and quantization
  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. 
Agnieszka B. Malinowska, Delfim F. M. Torres
math-ph math.MP math.OC