A study on the mild solution of impulsive fractional evolution equations

Xiao-Bao Shu and Yajing Shi

Applied Mathematics and Computation, 2016, vol. 273, issue C, 465-476

Abstract: 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.

Keywords: Impulsive differential equations; Caputo fractional derivative; Mild solutions; Fractional partial differential equations (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:273:y:2016:i:c:p:465-476

DOI: 10.1016/j.amc.2015.10.020

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