Local pseudo almost automorphic functions with applications to semilinear dynamic equations on changing-periodic time scales

In this paper, based on the concepts of changing-periodic time scales, we introduce a notion of local pseudo almost automorphic functions on an arbitrary time scale with a bounded graininess function μ. Then, some properties of local pseudo almost automorphic functions are investigated. As applications, by adopting the concept of a Π-semigroup on time scales, we obtain some new sufficient conditions for the existence of local pseudo almost automorphic mild solutions for a class of semilinear dynamic equations on arbitrary time scales.