n₀-order weighted pseudo Δ-almost automorphic functions and abstract dynamic equations

In this paper, we introduce the concept of a n₀-order weighted pseudo Δ _n0 ^δ-almost automorphic function under the matched space for time scales and we present some properties. The results are valid for q-difference dynamic equations among others. Moreover, we obtain some sufficient conditions for the existence of weighted pseudo Δ _n0 ^δ-almost automorphic mild solutions to a class of semilinear dynamic equations under the matched space. Finally, we end the paper with a further discussion and some open problems of this topic.