In the present paper, by using the Fibonacci difference matrix, we introduce the almost convergent sequence space $widehat{c}^{f}$. Also, we show that the spaces $widehat{c}^{f}$ and $widehat{c}$ are linearly isomorphic.
Further, we determine the $eta-$dual of the space $widehat{c}^{f}$ and characterize some matrix classses on this
space. Finally, Fibonacci core of a complex-valued sequence has been introduced, and we prove some inclusion theorems related to this new type of core.

Keywords: Sequence spaces, almost convergence, Fibonacci matrix, $eta$-dual, matrix transformations, core theorems