Torsion group schemes as iterative differential Galois groups

We show that torsion group schemes of abelian varieties in positive characteristic occur as iterative differential Galois groups of extensions of iterative differential fields. The main part is to find computable criteria when higher derivations are iterative derivations, and furthermore when an iterative derivation on the function field of an abelian variety is compatible with the addition map. For an explicit example, we give a construction of (a family of) such iterative derivations on the function field of an elliptic curve in characteristic two.