Heisenberg's equations of motion with fractional derivatives

Fractional variational principles is a new topic in the field of fractional calculus and it has been subject to intense debate during the last few years. One of the important applications of fractional variational principles is fractional quantization. In this present study, fractional calculus is applied to obtain the Hamiltonian formalism of non-conservative systems. The definition of Poisson bracket is used to obtain the equations of motion in terms of these brackets. The commutation relations and the Heisenberg equations of motion are also obtained. The proposed approach was tested on two examples and good agreements with the classical fractional are reported. Key words: Fractional calculus, fractional Hamiltonian, non-conservative systems, fractional Poisson brackets, Heisenberg equations, quantization