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| The fractional Riesz-Bessel equation with random innovations was
introduced in Angulo, Ruiz-Medina, Anh and Grechsch (2000), and
Angulo, Anh, McVinish and Ruiz-Medina (2005), for the bounded
(rectangle) and unbounded domain cases. In the case of random
initial conditions, a fractional version in time and in space was
derived in Anh and Leonenko (2001, 2002) in the case of unbounded
domain (see also the references therein).
In this paper we consider fractional Riesz Bessel equation on the
ball. Indeed, we assume that the time evolution of the propagator in
an open bounded connected domain is governed by a fractional
subdiffusion equation, whose fractional-orders of differentiation in
time and space lie in suitable intervals. Specifically,
Caputo-Djrbashian fractional derivative is used in time, and the
inverses of Riesz and Bessel potentials are considered in space. The
symmetry of the domain is exploited to deriving the explicit
solution to the associated eigenvalue problem, and hence, the
corresponding random solution. |
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