title: Variational principle for fractional kinetics and the Lévy Ansatz.
abstract: A variational principle is developed for fractional kinetics based on the auxiliary-field formalism. It is applied to the Fokker-Planck equation with spatiotemporal fractionality, and a variational solution is obtained with the help of the Lévy Ansatz. It is shown how the whole range from subdiffusion to superdiffusion is realized by the variational solution as a competing effect between the long waiting time and the long jump. The motion of the center of the probability distribution is also analyzed in the case of a periodic drift.
authors.affiliation: Department of Physical Engineering, Mie University, Mie 514-8507, Japan.
authors.forename: Sumiyoshi
authors.initials: S
authors.lastname: Abe