Tan, ElifYilmaz, SemihSahina, Murat2020-06-252020-06-252016closedAccess0960-07791873-2887https://doi.org/10.1016/j.chaos.2015.10.021https://hdl.handle.net/20.500.12587/6780In this paper, we present a new generalization of the Fibonacci quaternions that are emerged as a generalization of the best known quaternions in the literature, such as classical Fibonacci quaternions, Pell quaternions, k-Fibonacci quaternions. We give the generating function and the Binet formula for these quaternions. By using the Billet formula, we obtain some well-known results. Also, we correct some results in [3] and [4] which have been overlooked that the quaternion multiplication is non commutative. (C) 2015 Elsevier Ltd. All rights reserved.eninfo:eu-repo/semantics/closedAccessFibonacci sequenceGeneralized Fibonacci sequenceRecurrence relationsQuaternionsArticle821410.1016/j.chaos.2015.10.0212-s2.0-84946949765Q1WOS:000368227600001Q2