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).
2000 Mathematics Subject Classification: 26A33, 33E12, 33C60, 44A10,
45K05, 74D05,
The aim of this tutorial survey is to revisit the basic theory of relaxation
processes governed by linear differential equations of fractional order. The
fractional derivatives are intended both in the Rieamann-Liouville sense
and in the Caputo sense. After giving a necessary outline of the classica
theory of linear viscoelasticity, we contrast these two types of fractiona
derivatives in their ability...
2000 MSC: 26A33, 33E12, 33E20, 44A10, 44A35, 60G50, 60J05, 60K05.
After sketching the basic principles of renewal theory we discuss the
classical Poisson process and offer two other processes, namely the renewal
process of Mittag-Leffler type and the renewal process of Wright type, so
named by us because special functions of Mittag-Leffler and of Wright type
appear in the definition of the relevant waiting times. We compare these
three processes with each other, furthermore consider...
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