| 一类非线性分数阶边值问题正解的存在性 |
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| 引用本文： | 员陈鑫,蒋威. 一类非线性分数阶边值问题正解的存在性[J]. 阜阳师范学院学报(自然科学版), 2012, 29(1): 1-4 |
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| 作者姓名： | 员陈鑫 蒋威 |
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| 作者单位： | 安徽大学数学科学学院,安徽合肥,230039 |
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| 基金项目： | 国家自然科学基金项目，高校博士点专项科研基金，安徽省高校重大项目，安徽省高校自筹经费项目 |
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| 摘 要： | 研究了一类Caputo分数阶导数微分系统的边值问题解的存在性问题。先考察辅助系统的解的情况构造出Green函数,进而研究Green函数的性质来构造出紧算子。在较弱的条件下,通过运用锥不动点定理,可以得到该问题正解的存在性,并给出解的范围。
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| 关 键 词： | 分数阶微分方程 边值问题 Caputo导数 格林函数 不动点定理 |
Some existence results of solutions for nonlinear fractional boundary value problem |
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| YUAN Chen-xin,JIANG Wei. Some existence results of solutions for nonlinear fractional boundary value problem[J]. Journal of Fuyang Teachers College:Natural Science, 2012, 29(1): 1-4 |
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| Authors: | YUAN Chen-xin JIANG Wei |
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| Affiliation: | (School of Mathematical Science,Anhui University,Hefei Anhui 230039,China) |
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| Abstract: | The researched boundary value problem of nonlinear fractional order involving Caputo differentiation is investigated here.First we investigate the solution of the auxiliary system to find the Green function,and through discussing the characteristic of the Green function,we construct a compact operator.Under mild conditions,by means of some fixed-point theorems,some existence results of solutions for nonlinear fractional boundary value problem are obtained. |
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| Keywords: | fractional differential equation boundary value problem Caputo differentiation Green function fixed-point theorem. |
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