Fractional diffusion equation with distributed-order material derivative. Stochastic foundations

2015/10/01 by Magdziarz, Marcin, Teuerle, Marek
#26A33 #34A08 #60B05 #60F17 #60G50 #60G51 #60J75 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1510.00315

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.

Related

• Fractional material derivative: pointwise representation and a finite volume numerical scheme
• Time-fractional diffusion of distributed order
• Distributed order fractional sub-diffusion
• Monte Carlo Random Walk Simulations Based on Distributed Order Differential Equations
• Distributed-Order Fractional Kinetics