Subordination principle for fractional evolution equations

The abstract Cauchy problem for the fractional evolution equation Daa = Au, a > 0, (1) where A is a closed densely de??ned operator in a Banach space, is investigated. The subordination principle, presented earlier in [J. P r ??u s s, Evolutionary In- tegral Equations and Applications. Birkh??auser, Basel - Boston - Berlin (1993)] for general Volterra integral equations, is studied in detail for (1). Besides some additional properties of the subordinated solution operator, we discuss also some new aspects of this principle, such as invertibility, the inverse formula and the Feller semigroup of subordination operators