This author studies the three-point nonlinear discrete fractional boundary value problem
where and is continuous. The Green’s function associated to the above problem is derived and its properties are investigated. By using the Brouwer fixed point theorem and the Krasnoselski fixed point theorem, it is shown that a solution to the above problem exists. The results obtained in this paper generalize some recent results obtained by F. M. Atıcı and P. W. Eloe [“Two-point boundary value problems for finite fractional difference equations”, J. Difference Equ. Appl. 17, No. 4, 445–456 (2011; Zbl 1215.39002)].