  We develop fractional buffer layers (FBLs) to absorb propagating waves
without reflection in bounded domains. Our formulation is based on
variable-order spatial fractional derivatives. We select a proper
variable-order function so that dissipation is induced to absorb the coming
waves in the buffer layers attached to the domain. In particular, we first
design proper FBsL for the one-dimensional one-way and two-way wave
propagation. Then, we extend our formulation to two-dimensional problems, where
we introduce a consistent variable-order fractional wave equation. In each
case, we obtain the fully discretized equations by employing a spectral
collocation method in space and Crank-Nicolson or Adams-Bashforth method in
time. We compare our results with the perfectly matched layer (PML) method and
show the effectiveness of FBL in accurately suppressing any erroneously
reflected waves, including corner reflections in two-dimensional rectangular
domains. FBLs can be used in conjunction with any discretization method
appropriate for fractional operators describing wave propagation in bounded or
truncated domains.
