کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4626046 | 1631782 | 2016 | 12 صفحه PDF | دانلود رایگان |
This paper is concerned with the formula of mild solutions to impulsive fractional evolution equation. For linear fractional impulsive evolution equations [8–25,27,30,31], described mild solution as integrals over (tk,tk+1](k=1,2,…,m) and [0, t1]. 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 < α < 1 and 1 < α < 2, respectively; finally, we show that the reason that the solutions to an impulsive ordinary evolution equation are not distinct.
Journal: Applied Mathematics and Computation - Volume 273, 15 January 2016, Pages 465–476