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In \cite{Oz}, M. \"Ozdemir defined a new non-commutative number system calledhybrid numbers. In this paper, we define the hybrid Fibonacci and Lucasnumbers. This number system can be accepted as a generalization of the complex($\textbf{i}^{2}=-1$), hyperbolic ($\textbf{h}^{2}=1$) and dual Fibonaccinumber ($\varepsilon^{2}=0$) systems. Furthermore, a hybrid Fibonacci number isa number created with any combination of the complex, hyperbolic and dualnumbers satisfying the relation$\textbf{ih}=-\textbf{hi}=\varepsilon+\textbf{i}$. Then we used the Binet'sformula to show some properties of the hybrid Fibonacci numbers. We get somegeneralized identities of the hybrid Fibonacci and hybrid Lucas numbers.

Investigation of Generalized Hybrid Fibonacci Numbers and Their Properties