  In this note we propose the exact artificial boundary conditions formula to
the fractional reaction-subdiffusion equation on an unbounded domain. With the
application of Laplace transformation, the exact artificial boundary conditions
(ABCs) are derived to reformulate the original problem on the unbounded domain
to an initial-boundary-value problem on the bounded computational domain. By
the Kreiss theory, we prove that the reduced initial-boundary value problem is
stability. Based on the properties of tempered fractional calculus, we obtain
that the reduced initial-boundary value problem is long-time stability.
