Ulam's type stability analysis of fractional difference equation with impulse: Gronwall inequality approach

Authors: RABIA ILYAS, MUJEEB UR REHMAN

Abstract: In this paper, we present a new Gronwall inequality with an impulsive effect. The existence and uniqueness of the solution is investigated through fixed point theorems. Moreover, with the help of newly developed inequality Ulam's type stability criterion is developed for impulsive fractional difference equation. At last, a model is given to help the hypothetical outcome.

Keywords: Gronwall inequality, fractional difference equation, impulsive effect, existence and uniqueness, fixed point theorems; Ulam-Hyers-Rassias stability

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