  The analysis of the Rayleigh-B\'enard instability due to the mass diffusion
in a fluid-saturated horizontal porous layer is reconsidered. The standard
diffusion theory based on the variance of the molecular position growing
linearly in time is generalised to anomalous diffusion, where the variance is
modelled as a power-law function of time. A model of anomalous diffusion based
on a time-dependent mass diffusion coefficient is adopted, together with
Darcy's law, for momentum transfer, and the Boussinesq approximation, for the
description of the buoyant flow. A linear stability analysis is carried out for
a basic state where the solute has a potentially unstable concentration
distribution varying linearly in the vertical direction and the fluid is at
rest. It is shown that any, even slight, departure from the standard diffusion
process has a dramatic effect on the onset conditions of the instability. This
circumstance reveals a strong sensitivity to the anomalous diffusion index. It
is shown that subdiffusion yields instability for every positive mass diffusion
Rayleigh number, while superdiffusion brings stabilisation no matter how large
is the Rayleigh number. A discussion of the linear stability analysis based on
the Galilei-variant fractional-derivative model of subdiffusion is eventually
carried out.
