Some identities involving (p,q)-Fibonacci and Lucas quaternions

Abstract

In this study, we firstly examined the Horadam quaternions defined and studied by Halici and Karatas. Then, we used the Binet's formula to show some properties of the (p,q)-Fibonacci and Lucas quaternions. We also give some important identities including these quaternions. In this paper we have also contributed for the study of (p,q)-Fibonacci and Lucas quaternion sequence, deducing some of their identities using the Binet-style formula of Horadam quaternions. It is our intention to continue the study of this type of sequences, exploring some their applications in the science domain.