  The onset of the Rayleigh-Benard instability in a horizontal fluid layer is
investigated by assuming the fluid as a binary mixture and the concentration
buoyancy as the driving force. The focus of this study is on the anomalous
diffusion phenomenology emerging when the mean squared displacement of
molecules in the diffusive random walk is not proportional to time, as in the
usual Fick's diffusion, but it is proportional to a power of time. The
power-law model of anomalous diffusion identifies subdiffusion when the
power-law index is smaller than unity, while it describes superdiffusion when
the power-law index is larger than unity. This study reconsiders the stability
analysis of the Rayleigh-Benard problem by extending the governing equations to
include the anomalous diffusion.
