Journal of Applied Mathematics and Stochastic Analysis
Volume 2006 (2006), Article ID 93502, 18 pages
doi:10.1155/JAMSA/2006/93502
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.