  We explore the features of non-relativistic quantum tunneling in space
fractional quantum mechanics through a family of Cantor potentials. We consider
two types of potentials: general Cantor and general Smith-Volterra-Cantor
potential. The Cantor potential is an example of fractal potential while the
Smith-Volterra-Cantor potential doesn't belong to the category of a fractal
system. The present study brings for the first time, the study of quantum
tunneling through fractal potential in fractional quantum mechanics. We report
several new features of scattering in the domain of space fractional quantum
mechanics including the emergence of energy-band like features from these
systems and extremely sharp transmission features. Further the scaling relation
of the scattering amplitude with wave vector $k$ is presented analytically for
both types of potentials.
