| 分数阶积分微分方程多点边值问题解的存在性和唯一性 |
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| 引用本文： | 窦丽霞,刘锡平,金京福,王平友.分数阶积分微分方程多点边值问题解的存在性和唯一性[J].上海理工大学学报,2012,34(1):51-55. |
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| 作者姓名： | 窦丽霞 刘锡平 金京福 王平友 |
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| 作者单位： | 上海理工大学理学院,上海,200093 |
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| 基金项目： | 上海市教委科研创新基金，安徽省自然科学基金 |
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| 摘 要： | 研究一类非线性分数阶积分微分方程多点边值问题,通过计算边值问题的Green函数并分析Green函数的性质,利用压缩映射原理研究边值问题解的存在唯一性定理,并应用不动点定理得到了边值问题至少有一个解存在结论.同时给出了一个实例,说明所得结论.
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| 关 键 词： | 分数导数 积分微分方程 多点边值问题 不动点定理 压缩映射原理 存在性和唯一性 |
Existence and Uniqueness of Solutions of Multi point Boundary Value Problems for Integro differential Equations of Fractional Order |
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| DOU Li xi,LIU Xi ping,JIN Jing fu and WANG Ping you.Existence and Uniqueness of Solutions of Multi point Boundary Value Problems for Integro differential Equations of Fractional Order[J].Journal of University of Shanghai For Science and Technology,2012,34(1):51-55. |
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| Authors: | DOU Li xi LIU Xi ping JIN Jing fu and WANG Ping you |
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| Institution: | (College of Science.University of Shanghai for Science and Technology,Shanghai 200093,China ) |
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| Abstract: | The existence and uniqueness of solutions were investigated for a class of multi-point boundary value problems of nonlinear integro-differential equations with fractional derivatives.Via calculating the Green’s function and analyzing the properties of Green’s function,the existence of solutions for multi-point boundary value problems was studied based on the Banach contraction,principle and by applying,the fixed point theorem.An example was given to illustrate the results. |
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| Keywords: | fractional derivative integro-differential equation multi-point boundary value problem fixed point theorem contraction principle existence and uniqueness |
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