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In this paper, we present a new class of inequality of the Gronwall type anddiscuss some particular cases. In this sense, we investigate the uniqueness and$\delta$-Ulam-Hyers-Rassias stability of the mild solution for the fractionaldifferential equation with non-instantaneous impulses in a P$\delta$-normedBanach space.

A note on the mild solutions of Hilfer impulsive fractional differential equations