Discrete Laplace transform for interval-valued functions and its applications to interval fractional difference equations

Abstract

This work aims to present a discrete Laplace transform for handling interval fractional difference equations. We first deal with algebraic properties of the forward gH-difference operator for interval-valued functions. In particular, the forward gH-difference operator of the product of a real function and an interval-valued function is studied, which is then applied to establish summation by parts of interval-valued functions. Moreover, we present the new concept of discrete Laplace transform for interval-valued functions and study some relevant properties. The discrete Laplace transform formula on forward gH-difference operators is derived by applying summation by parts. Finally, the analytic solution of the interval Caputo fractional difference equations is established by means of the discrete Laplace transform. The results developed in this paper are illustrated through several numerical examples.