  Spin and charge fluctuations and superconductivity in Na_0.35CoO_2*1.3H_2O
are studied based on a multi-orbital Hubbard model. By applying the fluctuation
exchange (FLEX) approximation, we show that the Hund's-rule coupling between
the Co t2g orbitals causes ferromagnetic spin fluctuation. Triplet pairing is
favored by this ferromagnetic fluctuation on the hole-pocket band. We propose
that, in Na_0.35CoO_2*1.3H_2O, Co t2g orbitals and inter-orbital Hund's-rule
coupling play important roles on the triplet pairing, and this compound can be
a first example of the triplet superconductor mediated by
inter-orbital-interaction-induced ferromagnetic fluctuation.
