Circular-hyperbolic Fibonacci quaternions

Abstract

In this paper, circular-hyperbolic Fibonacci numbers and quaternions are defined. Also, some algebraic properties of circular-hyperbolic Fibonacci numbers and quaternions which are connected with circular-hyperbolic numbers and Fibonacci numbers are investigated. Furthermore, Honsberger's identity, the generating function, Binet's formula, d'Ocagne's identity, Cassini's identity, and Catalan's identity for these quaternions are given.