A generalized discrete fractional Gronwall inequality and its application on the uniqueness of solutions for nonlinear delay fractional difference system

In this paper, we state and prove a new discrete fractional version of the generalized Gronwall inequality. Based on this, a particular version expressed by means of discrete Mittag–Lefler functions is provided. As an application, we prove the uniqueness and obtain an estimate for the solutions of nonlinear delay Caputo fractional difference system. Numerical example is presented to demonstrate the applicability of the main results.

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