In this article we introduce binomial difference sequence spaces of fractional order $$\alpha ,$$ $$b_0^{r,s}\left( \Delta ^{(\alpha )}\right) ,$$ $$b_c^{r,s}\left( \Delta ^{(\alpha )}\right) $$ and $$b_{\infty }^{r,s}\left( \Delta ^{(\alpha )}\right) $$ by employing fractional difference operator $$\Delta ^{(\alpha )},$$ defined by $$\Delta ^{(\alpha )}x_k=\sum \limits _{i=0}^{\infty }(-1)^i\frac{\Gamma (\alpha +1)}{i!\Gamma (\alpha -i+1)}x_{k-i}.$$ We give some topological properties, obtain the Schauder basis and determine the $$\alpha -,$$ $$\beta -$$ and $$\gamma -$$ duals of the spaces. We characterize the matrix classes $$(b_c^{r,s}(\Delta ^{(\alpha )}),\ell _p),$$ $$(b_c^{r,s}(\Delta ^{(\alpha )}),\ell _{\infty })$$ and $$(b_c^{r,s}(\Delta ^{(\alpha )}),c).$$ We characterize certain classes of compact operators on the space $$b_c^{r,s}(\Delta ^{(\alpha )})$$ using Hausdorff measure of non-compactness. Finally, we present the graphical interpretation of the operator $$B^{r,s}\left( \Delta ^{(\alpha )}\right) $$ .