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 spatio-temporal 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.

13 pages, no figures

References in corpus (4)

• Understanding individual human mobility patterns
• The scaling laws of human travel
• Fractional Fokker-Planck dynamics: Numerical algorithm and simulations
• Operator solutions for fractional Fokker-Planck equations

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