The purpose of this paper is to introduce the notion of \(\vartheta \) pseudo S-asymptotically \(\mathcal {T}-\) omega periodic functions and their applications. First, we present the new concept of \(\vartheta -\) pseudo S-asymptotically \(\mathcal {T}-\) omega periodic functions. In addition, we study some qualitative properties of this class. Then, we establish the existence and uniqueness of \(\vartheta -\) pseudo S-asymptotically \(\mathcal {T}-\) omega periodic mild solutions for abstract neutral functional differential equations with finite delay by applying Picard’s fixed point theorem. Finally, we provide an application to illustrate the effectiveness of the results.
