  This article is on the inverse Galois problem in Galois theory of linear
iterative differential equations in positive characteristic. We show that it
has an affirmative answer for reduced algebraic group schemes over any
iterative differential field which is finitely generated over its algebraically
closed field of constants. We also introduce the notion of equivalence of
iterative derivations on a given field - a condition which implies that the
inverse Galois problem over equivalent iterative derivations are equivalent.
