Interval discrete fractional calculus and its application to interval fractional difference equations

In this work, we present some useful results of discrete fractional calculus for interval-valued functions. The composition rules for interval fractional operators are introduced, which are used to construct the general form of the solutions to nonlinear interval fractional difference equations. An illustrative example is provided in which the method of recursive iterations is applied to obtain explicit formulas for the solutions of linear interval fractional difference equations.