  Using the Sierpinski gasket (triangle) and carpet (square) lattices as
examples, we theoretically study the properties of fractal superconductors. For
that, we focus on the phenomenon of $s$-wave superconductivity in the Hubbard
model with attractive on-site potential and employ the Bogoliubov-de Gennes
approach and the theory of superfluid stiffness. For the case of the Sierpinski
gasket, we demonstrate that fractal geometry of the underlying crystalline
lattice can be strongly beneficial for superconductivity, not only leading to a
considerable increase of the critical temperature $T_c$ as compared to the
regular triangular lattice but also supporting macroscopic phase coherence of
the Cooper pairs. In contrast, the Sierpinski carpet geometry does not lead to
pronounced effects, and we find no substantial difference as compared with the
regular square lattice. We conjecture that the qualitative difference between
these cases is caused by different ramification properties of the fractals.
