PSEUDO ASYMPTOTIC SOLUTIONS OF FRACTIONAL ORDER SEMILINEAR EQUATIONS

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 D(t)(alpha+1)tu(t) + mu D(t)(beta)u(t) - Au(t) = f(t,u(t)), t > 0, 0 < alpha <= beta <= 1, mu >= 0, 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 P-0(R+, X) := {phi epsilon BC(R+, X) : lim(T ->infinity) 1/T integral(T)(0) parallel to phi(s)parallel to ds = 0}. Moreover, this decomposition is unique.