In this paper, we establish variation of constant formulas for both Caputo and Riemann- Liouville fractional difference equations. The main technique is the Z -transform. As an application, we prove a lower bound on the separation between two different solutions of a class of nonlinear scalar fractional difference equations.

KW - fractional difference equation KW - variation of constant KW - separation of solutions T1 - Variation of constant formulas for fractional difference equations