脉冲分数阶发展方程温和解的新研究
A new study on the mild solution for impulsive fractional evolution equations
摘要：
本文考虑一类$0<α<1$阶脉冲分数阶发展方程的温和解.在分析了Mittag-Leffer函数和$α$ -预解算子理论的分析结果后，用$S_α(t)S_α^{-1}(t_i)$代替脉冲项算子$S_α(t-t_i)$，给出了脉冲分数阶发展方程温和解的一个新的定义，其中$S_α^{-1}(t_i)$表示分数阶解算子$S_α(t)$在$t=t_i, (i=1,2,\cdots m)$的逆.
英文摘要：
In this article, we consider 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 $t=t_i, (i=1,2,\cdots m)$.
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