  Palatini $F(R)$ gravity proved to be a powerful tool in order to realize
asymptotically flat inflaton potentials. Unfortunately, it also inevitably
implies higher-order inflaton kinetic terms in the Einstein frame that might
jeopardize the evolution of the system out of the slow-roll regime. We prove
that a $F(R+X)$ gravity, where $X$ is the inflaton kinetic term, solves the
issue. Moreover, when $F$ is a quadratic function such a choice easily leads to
a new class of inflationary attractors, fractional attractors, that generalizes
the already well-known polynomial $\alpha$-attractors.
