Explicit solutions of some fractional partial differential equations via stable subordinators

Debbi, Latifa

doi:https://doi.org/10.1155/JAMSA/2006/93502

International Journal of Stochastic Analysis

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Volume 2006 | Article ID 093502 | https://doi.org/10.1155/JAMSA/2006/93502

Explicit solutions of some fractional partial differential equations via stable subordinators

Latifa Debbi^1,2,3

Received10 Dec 2004

Revised05 May 2005

Accepted10 May 2005

Published26 Feb 2006

Abstract

The aim of this work is to represent the solutions of one-dimensional fractional partial differential equations (FPDEs) of order (α∈ℝ+\ℕ) in both quasi-probabilistic and probabilistic ways. The canonical processes used are generalizations of stable Lévy processes. The fundamental solutions of the fractional equations are given as functionals of stable subordinators. The functions used generalize the functions given by the Airy integral of Sirovich (1971). As a consequence of this representation, an explicit form is given to the density of the 3/2-stable law and to the density of escaping island vicinity in vortex medium. Other connected FPDEs are also considered.

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Copyright

Copyright © 2006 Latifa Debbi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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