  In this paper, we present a further generalization of the bi- periodic
Fibonacci quaternions and octonions. We give the generating function, the Binet
formula, and some basic properties of these quaternions and octonions. The
results of this paper not only give a generalization of the bi-periodic
Fibonacci quaternions and octonions, but also include new results such as the
matrix representation and the norm value of the generalized bi-periodic
Fibonacci quaternions.
