Yağmur, Tülay2021-11-122021-11-122020-06-30https://doi.org/10.31801/cfsuasmas.582674http://hdl.handle.net/20.500.12575/76038In this paper, we introduce a new quaternion sequence called hyperbolic (p,q)-Fibonacci quaternions. This new quaternion sequence includes hyperbolic Fibonacci, hyperbolic k-Fibonacci, hyperbolic Pell, hyperbolic k-Pell, hyperbolic Jacobsthal, hyperbolic k-Jacobsthal quaternions. We give generating function and Binet formula for these quaternions. We also obtain some identities such as d'Ocagne's, Catalan's and Cassini's identities involving hyperbolic (p,q)-Fibonacci quaternions.enFibonacci numbers(p;q)-Fibonacci numbers(p;q)-Fibonacci quaternionsArticle6918808902618-6470