  For three different geometric configurations of matter and two different
thermodynamic equations of state, low angular momentum, multi-transonic,
axially symmetric accretion flow of matter having fractional dimension of mass
distribution onto a rotating black hole has been studied by employing certain
post-Newtonian pseudo-Kerr black hole potential. Such task has been
accomplished mathematically by mapping the fractal nature of accreted medium
onto its continuum counterpart. The difference between spin dependence of
accretion dynamics of the fractal medium and the continuous medium has been
highlighted. By employing a time dependent linear perturbation scheme, it has
been demonstrated that accretion of matter with fractional dimension of density
distribution can be considered as a natural example of classical analogue
model. The corresponding acoustic surface gravity has been estimated in terms
of accretion variables. The value of the surface gravity changes as the
accreted matter makes a transition from its fractal nature to the corresponding
continuum distribution.
