Yağmur, Tülay2021-07-012021-07-0120201303-59912618-6470https:/dx.doi.org/ 10.31801/cfsuasmas.582674https://hdl.handle.net/20.500.12451/8236In 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's 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.eninfo:eu-repo/semantics/openAccessFibonacci Numbers(p, q)-Fibonacci Numbers(p, q)-Fibonacci QuaternionsHyperbolic QuaternionsHyperbolic (p, q)-Fibonacci QuaternionsArticle69188089010.31801/cfsuasmas.582674N/A