  Let X be a normal affine T-variety of complexity at most one over a perfect
field k, where T stands for the split algebraic torus. Our main result is a
classification of additive group actions on X that are normalized by the
T-action. This generalizes the classification given by the second author in the
particular case where k is algebraically closed and of characteristic zero.
  With the assumption that the characteristic of k is positive, we introduce
the notion of rationally homogeneous locally finite iterative higher
derivations which corresponds geometrically to additive group actions on affine
T-varieties normalized up to a Frobenius map. As a preliminary result, we
provide a complete description of these additive group actions in the toric
situation.
