Gronwall inequality for the discrete generalized proportional fractional derivative

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Abstract

We established a new Gronwall inequality for the discrete generalized proportional fractional derivative. The result extended known discrete fractional inequalities and provided explicit bounds, uniqueness criteria, and Ulam–Hyers stability for nonlinear delayed fractional systems. An example was provided to illustrate the theory.

Keywords

discrete generalized proportional fractional derivative / discrete Gronwall inequality / delay fractional difference system / bound for the solution / Ulam–Hyers stability

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