期刊
APPLIED MATHEMATICS AND COMPUTATION
卷 273, 期 -, 页码 465-476出版社
ELSEVIER SCIENCE INC
DOI: 10.1016/j.amc.2015.10.020
关键词
Impulsive differential equations; Caputo fractional derivative; Mild solutions; Fractional partial differential equations
资金
- Hunan Provincial Natural Science Foundation of China [14JJ2050]
This paper is concerned with the formula of mild solutions to impulsive fractional evolution equation. For linear fractional impulsive evolution equations [8-25,27,30,311, described mild solution as integrals over (t(k), t(k+1)] (k = 1, 2,..., m) and [0, t(1)]. On the other hand, in [26,28,29], their solutions were expressed as integrals over [0,t]. However, it is still not clear what are the correct expressions of solutions to the fractional order impulsive evolution equations. In this paper, firstly, we prove that the solutions obtained in [8-25,27,30,31] are not correct; secondly, we present the right form of the solutions to linear fractional impulsive evolution equations with order 0 < alpha < 1 and 1 < alpha < 2, respectively; finally, we show that the reason that the solutions to an impulsive ordinary evolution equation are not distinct. (C) 2015 Elsevier Inc. All rights reserved.
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