Discrete Gronwall’s inequality for Ulam stability of delay fractional difference equations

Abstract

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.

Keywords

• delay fractional difference equations
• discrete Gronwall’s inequality
• uniqueness of solution
• Ulam stability