Xiao-Bao Shu1, Linxin Shu, And Fei Xu. A New Study on the Mild Solution for Impulsive Fractional Evolution Equations. Dynamic Systems and Applications 29 (2020) No.12, 3317-3332

https://doi.org/10.46719/dsa202029122

ABSTRACT.
In this article, we consider the mild solutions to a class of impulsive fractional evolution equations of order 0 < α < 1. After analyzing analytic results reported in the literature using Mittag-Leffer function, α-resolvent operator theory, we propose a more appropriate new definition of mild solutions for impulsive fractional evolution equations by replacing the impulse term operator S_α(t − t_i) with S_α(t)S_α⁻¹(t_i), where S_α⁻¹(t_i) denotes the inverse of the fractional solution operator S_α(t) at t = t_i, (i = 1,2,···m).

AMS (MOS) Subject Classification. 34A08, 26A33, 34K45.