Almost automorphic solutions to non-autonomous dynamic equations with Stepanov-like almost automorphic forcing terms on time scales

In this article, we generalize the concept of Stepanov-like almost automorphic functions on time scales and present some properties including the composition theorem. Based on it, some results on the existence and uniqueness of almost automorphic solution to non-autonomous dynamic equations with Stepanov-like almost automorphic forcing terms on time scales are established. In our results, we do not need to assume the uniform Lipschitz condition of the nonlinear forcing term and do not need to assume that the Green's function is Bi-automorphic directly. Finally, an application to Lasota-Wazewska model on time scales is provided. For more information see https://ejde.math.txstate.edu/Volumes/2025/87/abstr.html