| 刘玉记.具有脉冲的分数阶Bagley-Torvik 模型边值问题[J].数学年刊A辑,2018,39(3):309~330 |
| 具有脉冲的分数阶Bagley-Torvik 模型边值问题 |
| Boundary Value Problems for Fractional Order Bagley-Torvik Models with Impulse Effects |
| Received:November 26, 2015 Revised:July 12, 2017 |
| DOI：10.16205/j.cnki.cama.2018.0027 |
| 中文关键词: 脉冲分数阶Bagley-Torvik微分方程, 边值问题, Schaefer不动点定理 |
| 英文关键词:Impulsive fractional order Bagley-Torvik differential equation, Boundary value problem, Schaefer's fixed point theorem |
| 基金项目:本文受到广东省自然科学基金(No.S2011010001900)和广州市科技计划项目(No.201804010350)的资助. |
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| 中文摘要: |
| 将具有脉冲的分数阶Bagley-Torvik微分方程边值问题巧妙地转化为积分方程,
定义加权Banach空间及全连续算子, 运用不动点定理获得该边值问题解的存在性定理.
举例说明了定理的应用. 最后提出有趣的研究问题. |
| 英文摘要: |
| The author converts the boundary value problem for impulsive fractional order Bagley-Torvik
differential equation to an integral equation technically (a new method). By defining a weighted
function Banach space and a completely continuous operator, some existence results for solutions
are established. This analysis relies on the well known Schauder's fixed point theorem. Examples
are given to illustrate the main results. |
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