On the concept and existence of solution for impulsive fractional differential equations
On the concept and existence of solution for impulsive fractional differential equations
复制标题
论脉冲分数阶微分方程解的概念及存在性
DOI：
10.1016/j.cnsns.2011.11.017
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发表时间：
2012-07-01
影响因子：
3.9
通讯作者：
Wang, JinRong
中科院分区：
文献类型：
--
作者：
Feckan, Michal;Zhou, Yong;Wang, JinRong
本文的灵感来自于最近几篇关于分数阶导数脉冲微分方程解的存在性问题的论文。我们首先证明了被引论文的解公式是不正确的。其次，我们重新考虑了一类脉冲分数阶微分方程，并引入了具有Caputo分数阶导数的脉冲Cauchy问题的正确解公式。进一步利用不动点方法，建立了该问题解存在的充分条件。给出了一些例子来说明结果。(C) 2011 Elsevier B.V.版权所有
This paper is motivated from some recent papers treating the problem of the existence of a solution for impulsive differential equations with fractional derivative. We firstly show that the formula of solutions in cited papers are incorrect. Secondly, we reconsider a class of impulsive fractional differential equations and introduce a correct formula of solutions for a impulsive Cauchy problem with Caputo fractional derivative. Further, some sufficient conditions for existence of the solutions are established by applying fixed point methods. Some examples are given to illustrate the results. (C) 2011 Elsevier B.V. All rights reserved.