Discrete Gronwall’s inequality for Ulam stability of delay fractional difference equations - Shu-Yu Yang; Guo-Cheng Wu (Mathematical Modelling and Analysis)
This paper investigates Ulam stability of delay fractional difference equations. First, a useful equality of double fractional sums is employed and discrete Gronwall’s inequality of delay type is provided. A delay discrete-time Mittag-Leffler function is used and its non-negativity condition is given. With the solutions’ existences, Ulam stability condition is presented to discuss the error estimation of exact and approximate solutions.