  In this paper we introduce a discrete fractional resolvent family
$\{S_{\alpha,\beta}^n\}_{n\in\mathbb{N}_0}$ generated by a closed linear
operator in a Banach space $X$ for a given $\alpha,\beta>0.$ Moreover, we study
its main properties and, as a consequence, we obtain a method to study the
existence and uniqueness of the solutions to discrete fractional difference
equations in a Banach space.
