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The aim of the paper is to introduced the spaces $c_{0}^{\lambda}(\hat{F})$and $c^{\lambda}(\hat{F})$ which are the BK-spaces of non-absolute type andalso derive some inclusion relations. Further, we determine the$\alpha-,\beta-,\gamma-$duals of those spaces and also construct their bases.We also characterize some matrix classes on the spaces$c_{0}^{\lambda}(\hat{F})$ and $c^{\lambda}(\hat{F}).$ Here we characterize thesubclasses $\mathcal{K}(X,Y)$ of compact operators where $X$ is$c_{0}^{\lambda}(\hat{F})$ or $c^{\lambda}(\hat{F})$ and $Y$ is one of thespaces $c_{0},c, l_{\infty}, l_{1}, bv$ by applying Hausdorff measure ofnoncompactness.

Some new Fibonacci difference spaces of non-absolute type and compact operators