  We investigate the fully nonlinear model for convection in a Darcy porous
material where the diffusion is of anomalous type as recently proposed by
Barletta. The fully nonlinear model is analysed but we allow for variable
gravity or penetrative convection effects which result in spatially dependent
coefficients. This spatial dependence usually requires numerical solution even
in the linearized case. In this work we demonstrate that regardless of the size
of the Rayleigh number the perturbation solution will decay exponentially in
time for the superdiffusion case. In addition we establish a similar result for
convection in a bidisperse porous medium where both macro and micro porosity
effects are present. Moreover, we demonstrate a similar result for
thermosolutal convection.
