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In this paper, with the help of higher order Fibonacci numbers, we introduce higher order Fibonacci quaternions that generalize the Fibonacci quaternions studied by Horadam and Halici. We give recurrence relation, Binet formula, generating and exponential generating functions and some other algebraic properties of higher order Fibonacci quaternions.

This paper deals with developing a new class of quaternions, octonions and sedenions called higher order Fibonacci 2 m -ions (or-higher order Fibonacci hyper complex numbers) whose components are higher order Fibonacci numbers. We give recurrence relation, Binet formula, generating function and exponential generating function of higher order Fibonacci 2 m -ions. We also derive some identities such as Vajda’s identity, Catalan’s identity, Cassini’s identity, and d’Ocagne’s identity with the aid of the Binet formula. Finally, we develop some matrix identities involving higher order Fibonacci 2 m -ions which allow us to obtain some properties of these higher order hyper complex numbers.