Results of Semigroup of Linear Operators Generating a General Class of Semilinear Initial Value Problems

This paper present results of ω-order preserving partial contraction mapping generating a general class semilinear initial value problems. We consider the use fractional powers unbounded linear operators for its application by starting with some concerning such powers. assume A to be infinitesimal generator an analytic semigroup in Banach space X, 0 ∈ ρ(A) and defined < α ≤ 1. also show that Aα is closed operator whose domain D(Aα) ⊃ D(A) dense X. Finally we established bounded, continuous Holder continuous.