A novel delayed discrete fractional Mittag-Leffler function: representation and stability of delayed fractional difference system

Abstract

In this paper, a delayed discrete Mittag-Leffler matrix function generated by two noncommutative square matrices is introduced. Utilizing this function, the paper establishes an explicit expression for solving constant delay fractional difference systems. Additionally, a criterion for determining the Ulam-Hyers stability of delay fractional difference systems with constant coefficients is derived using the aforementioned explicit representation formula.