On the application of Riemann–Liouville fractional calculus to the analysis of probability distributions

In this paper some issues of application of Riemann–Liouville operators to the analysis of absolutely continuous distributions are considered. In general case such transition considerably change common properties of probability densities, making standard statistical techniques infeasible. It is shown that Fokker–Planck equation may have multiple analogues of fractional order. It is also demonstrated that fractional equations of Fokker–Planck type do not permit ordinary hydrodynamical substitution.