On split Narayana and Narayana–Lucas hybrid quaternions

In this paper, we introduce the novel concepts of split Narayana quaternions and split Narayana–Lucas quaternions within the innovative framework of hybrid numbers. We explore their deep connections with Narayana and Narayana–Lucas quaternions, uncovering new perspectives in this mathematical domain. Furthermore, we establish several fundamental properties, including recurrence relations, Binet formulas, generating functions, exponential generating functions, and other significant identities associated with these newly defined quaternions. Finally, to better illustrate these theoretical findings, we also provide a numerical simulation of split Narayana quaternions and split Narayana–Lucas hybrid quaternions.