  A class of perturbative charged rotating dilaton black hole solutions coupled
to the nonlinear Born-Infeld electrodynamics is presented. The strategy for
obtaining these solutions is to start from Myers-Perry solutions, and then
considering the effects of the dilaton field, Born-Infeld parameter as well as
the electric charge as a perturbative parameter. We perform the perturbations
up to 4th order in the extremal black holes of Einstein-Born-Infeld-dilaton
gravity with equal angular momentum and arbitrary dilaton coupling constant. We
discuss the physical properties of these black holes and study their dependence
on the perturbative parameter $q$, the dilaton coupling constant $\alpha$ and
the Born-Infeld parameter $\beta$. One can see these black holes solutions
satisfy a generalized Smarr relation.
