Abstract:

Using fixed point theorem in metric space, the authors studied the existence of positive and nondecreasing solution for a class of the fractional difference equations with fractional boundary conditions. With the aid of some characteristics of the Green’s function, we obtained sufficient conditions for the existence of a unique nonnegative and nondecreasing solution to this class of equations. And we discussed the existence and uniqueness of a positive and strictly increasing solution to this equations.

Key words: fractional boundary conditions, Green’s function, strictly increasing