Pseudo asymptotic solutions of fractional order semilinear equations

Abstract

Using a generalization of the semigroup theory of linear operators, we prove existence and uniqueness of mild solutions for the semilinear fractional order differential equation [mathematical equation] with the property that the solution can be written as u = f+h where f belongs to the space of periodic (resp. almost periodic, compact almost automorphic, almost automorphic) functions and h belongs to the space [mathematical equation]. Moreover, this decomposition is unique.