  The isotope effects for Fe based superconductors are considered by including
the phonon and magnetic fluctuations within the two band Eliashberg theory. We
show that the recently observed inverse isotope effects of Fe, $\alpha_{Fe}
\approx -0.18 \pm 0.03 $,\cite{Shirage0903.3515} as well as the large positive
isotope exponent ($\alpha\approx 0.35$) can naturally arise for the
magnetically induced sign revered s-wave pairing state within reasonable
parameter range. Either experimental report can not be discarded from the
present analysis based on the parameter values they require. The inverse and
positive isotope effects mean, respectively, the interband and intraband
dominant eletron-phonon interaction. We first make our points based on the
analytic result from the square well potential model and present explicit
numerical calculations of the two band Eliashberg theory.
