Mathematics Subject Classification: 26A33, 47B06, 47G30, 60G50, 60G52, 60G60.
In this paper the multi-dimensional analog of the Gillis-Weiss random walk model is studied. The convergence of this random walk to a fractional diffusion process governed by a symmetric operator defined as a hypersingular integral or the inverse of the Riesz potential in the sense of distributions is proved.
* Supported by German Academic Exchange Service (DAAD).

MSC 2010: 26A33, 35R11, 35R60, 35Q84, 60H10 Dedicated to 80-th anniversary of Professor Rudolf Gorenflo
There is a well-known relationship between the Itô stochastic differential equations (SDEs) and the associated partial differential equations called Fokker-Planck equations, also called Kolmogorov equations. The Brownian motion plays the role of the basic driving process for SDEs. This paper provides fractional generalizations of the triple relationship between the driving process,...

Mathematics Subject Classification: 35CXX, 26A33, 35S10
The well known Duhamel principle allows to reduce the Cauchy problem for linear inhomogeneous partial differential equations to the Cauchy
problem for corresponding homogeneous equations. In the paper one of the possible generalizations of the classical Duhamel principle to the time-fractional pseudo-differential equations is established.
* This work partially supported by NIH grant P20 GMO67594.

Mathematics Subject Classification: 65C05, 60G50, 39A10, 92C37
In this paper the multi-dimensional Monte-Carlo random walk simulation
models governed by distributed fractional order differential equations
(DODEs) and multi-term fractional order differential equations are constructed.
The construction is based on the discretization leading to a generalized
difference scheme (containing a finite number of terms in the time
step and infinite number of terms in the space step) of the...

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