Weighted Almost Automorphic Behavior Of Solutions To A Fractional Evolution Equation

In this paper, we investigate the existence and uniqueness of μ-pseudo almost auto-morphic and weighted pseudo almost automorphic mild solutions to a semilinear fractional differential equation. where A is a closed linear operator defined on Banach space X, a ∈L1loc(R+) is a scalar-valued kernel,f:R×X â†' X belongs to a closed subspace of the space of continuous and bounded functions satisfying some Lipschitz type conditions, and for α> 0, the fractional derivative is understood in the sense of Weyl.Our main results are based upon some ergodicity and composition theorems of pseudo almost automorphic functions combined with fixed point techniques. This thesis are di-vided into four sections.