Abstract

We study almost automorphic (mild) solutions of the semilinear fractional equation ∂t α u = A u + ∂t α - 1 f ({dot operator}, u), 1 < α < 2, considered in a Banach space X, where A is a linear operator of sectorial type ω < 0. We prove the existence and uniqueness of an almost automorphic mild solution assuming that f (t, x) is almost automorphic in t for each x ∈ X, satisfies some Lipschitz type conditions and takes values on X. © 2008 Elsevier Ltd. All rights reserved.