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| 拟线性分数阶高阶脉冲微分方程边值问题解的存在性 | |
| 引用本文： | 杨军,刘东利,张波.拟线性分数阶高阶脉冲微分方程边值问题解的存在性[J].中山大学学报(自然科学版),2014,53(1). |
| 作者姓名： | 杨军 刘东利 张波 |
| 作者单位： | 1. 燕山大学理学院, 河北 秦皇岛 066004； 2. 河北省数学研究所, 河北 石家庄 050000 |
| 基金项目： | 国家自然科学基金资助项目(60604004);河北省应用基础研究计划重点基础研究资助项目(13961806D);秦皇岛市科技支撑计划资助项目(201001A037,201101A168) |
| 摘 要： | 研究了以下一类拟线性分数阶高阶脉冲微分方程边值问题{Dq0+y(t)=A(t,y)y(t)+f(t,y(t),Φy(t),Ψy(t)),■t∈0,1],q∈(n-1,n],y(i)(0)=0,Δy(i)|t=tk=0,1≤i≤n-2,k=1,2,…,p,Δy|t=tk=Ik(y(t k)),Δy(n-1)|t=tk=Jk(y(tk)),k=1,2,…,p,y(0)=y0+g(y),y(n-1)(1)=y1+∑m-2j=1bjy(n-1)(ξj)解的存在性。通过定义一个压缩映射并利用Banach不动点定理和Krasnoselskii's不动点定理,得到了边值问题存在唯一解和至少存在一个解的充分条件,最后分别给出一个例子来验证主要结果。 |
| 关 键 词： | 分数阶微分方程 高阶 脉冲 Caputo分数阶导数 不动点定理 |
| 收稿时间： | 2013-04-16; |
Existence of Solutions for High-order Impulsive Boundary Value Problem of Quasilinear Fractional Differential Equation |
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| YANG Jun,LIU Dongli,ZHANG Bo.Existence of Solutions for High-order Impulsive Boundary Value Problem of Quasilinear Fractional Differential Equation[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2014,53(1). | |
| Authors: | YANG Jun LIU Dongli ZHANG Bo |
| Institution: | 1. College of Science, Yanshan University, Qinhuangdao 066004, China; 2. Mathematics Research Center in Hebei Province, Shijiazhuang 050000, China |
| Abstract: | The existence of solutions for high-order impulsive boundary value problem of Caputo fractional differential equation in the form Dq0+y(t) = A(t,y)y(t)+f(t,y(t),Φy(t),Ψy(t)),t∈［0,1］,q∈(n－1,n), y(i)(0)=0, Δy(i) | t=tk = 0, 1≤i≤n－2,k=1,2,…,p, Δy | t=tk = Ik (y(tk)), Δy(n－1) | t=tk = Jk (y(t k)),k=1,2,…,p, y(0) = y0+ g(y), y(n－1)(1) = y1+∑m－2 j=1 bj y(n－1) (ξj) is studied. By defining a contraction mapping and using the fixed point theorems, some sufficient conditions for the existence of one unique solution and at least a solution are established. Further, two examples are presented to illustrate the main results respectively. |
| Keywords: | fractional differential equations high-order impulsive Caputo fractional derivative fixed point theorems |
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