Fractional diffusion equation with distributed-order material derivative. Stochastic foundations
Probability
2015-10-02 v1
Abstract
In this paper we present stochastic foundations of fractional dynamics driven by fractional material derivative of distributed order-type. Before stating our main result we present the stochastic scenario which underlies the dynamics given by fractional material derivative. Then we introduce a Levy walk process of distributed-order type to establish our main result, which is the scaling limit of the considered process. It appears that the probability density function of the scaling limit process fulfills, in a weak sense, the fractional diffusion equation with material derivative of distributed-order type.
Cite
@article{arxiv.1510.00315,
title = {Fractional diffusion equation with distributed-order material derivative. Stochastic foundations},
author = {Marcin Magdziarz and Marek Teuerle},
journal= {arXiv preprint arXiv:1510.00315},
year = {2015}
}