Discrete fractional calculus for interval–valued systems

Abstract

This study investigates linear fractional difference equations with respect to interval–valued functions. Caputo and Riemann–Liouville differences are defined. w–monotonicity is introduced and discrete Leibniz integral laws are provided. Then exact solutions of two linear equations are obtained by Picard's iteration. In comparison with the deterministic initial problems, the solutions are given in discrete Mittag–Leffler functions with and without delay, respectively. This paper provides a novel tool to understand fractional uncertainty problems on discrete time domains.