Accelerating subdiffusions governed by multiple-order time-fractional diffusion equations: Stochastic representation by a subordinated Brownian motion and computer simulations

摘要

We study anomalous diffusion governed by the n-tuple order time-fractional Fokker-Planck equation ofnRiemann-Liouville type. We find a stochastic representation of this anomalous diffusion; that is, the stochasticnprocess with probability density function evolving according to the considered diffusion equation. The stochasticnrepresentation, given in the form of the Brownian motion subordinated by a L´evy process defined in termsnof the L´evy exponent, is shown to be an accelerating subdiffusion process. Taking advantage of the stochasticnrepresentation, we construct an algorithm for computer simulations of the accelerating-subdiffusion sample paths.nMoreover, we obtain a stochastic representation and the simulation algorithm for the case of the anomalousndiffusion influenced by an external space-dependent force field.