  A fractional generalization of the Floquet theorem is suggested for
fractional Schr\"odinger equations (FTSE)s with the time-dependent periodic
Hamiltonians. The obtained result, called the fractional Floquet theorem (fFT),
is formulated in the form of the Mittag-Leffler function, which is considered
as the eigenfunction of the Caputo fractional derivative. The suggested formula
makes it possible to reduce the FTSE to the standard quantum mechanics with the
time-dependent Hamiltonian, where the standard Floquet theorem is valid. Two
examples related to quantum resonances are considered as well to support the
obtained result.
