Existence and controllability of p-th Weyl almost automorphic solutions for non-autonomous neutral FDEs

This paper studies the existence and controllability of p-th Weyl almost automorphic solutions for a class of non-autonomous neutral functional differential equations with finite delay. By utilising the theory of linear evolution operators and Banach fixed point theorem we first discuss the existence of p-th Weyl almost automorphic solutions for the considered equation and obtain sufficient conditions for the existence, uniqueness, and globally exponential stability of the p-th Weyl almost automorphic solutions. Then we further prove that the corresponding control system is approximately controllable by the p-th Weyl almost automorphic solutions under some conditions. In the end, an example is provided to demonstrate the obtained results.