Properties of generalized commutative third-order Jacobsthal quaternions

Generalized commutative quaternions generalize elliptic, parabolic and hyperbolic quaternions, bicomplex numbers, complex hyperbolic numbers and hyperbolic complex numbers. In this paper, we study generalized commutative third-order Jacobsthal quaternions and generalized commutative modified third-order Jacobsthal quaternions. Furthermore, we present some properties of these numbers and relations between them.