On the stability of exact ABCs for the reaction-subdiffusion equation on unbounded domain

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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.