| 一类含参数分数阶微分方程边值问题正解的性质研究 |
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| 引用本文： | 冯海星,翟成波.一类含参数分数阶微分方程边值问题正解的性质研究[J].应用数学和力学,2017,38(7):818-826. |
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| 作者姓名： | 冯海星 翟成波 |
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| 作者单位： | 1山西财经大学 应用数学学院, 太原 030031;2山西大学 数学科学学院,太原 030006 |
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| 基金项目： | The National Natural Science Foundation of China(11201272)国家自然科学基金(11201272)，山西省自然科学基金(2015011005)，2015山西省131人才项目 |
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| 摘 要： | 研究了一类含参数的分数阶微分方程边值问题，主要运用锥上的不动点定理及混合单调算子特征值问题的性质得出了正解关于参数的性质:存在唯一性、单调性、连续性以及极限性质.最后举例说明了结果的可行性.
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| 关 键 词： | 分数阶微分方程 正解 存在唯一性 参数 混合单调算子 |
| 收稿时间： | 2017-05-05 |
Properties of Positive Solutions to a Class of Fractional Differential Equations With Parameters and Integral Boundary Conditions |
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| FENG Hai-xing,ZHAI Cheng-bo.Properties of Positive Solutions to a Class of Fractional Differential Equations With Parameters and Integral Boundary Conditions[J].Applied Mathematics and Mechanics,2017,38(7):818-826. |
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| Authors: | FENG Hai-xing ZHAI Cheng-bo |
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| Institution: | 1College of Applied Mathematics, Shanxi University of Finance and Economics,Taiyuan 030031, P.R.China;2School of Mathematical Sciences,Shanxi University, Taiyuan 030006, P.R.China |
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| Abstract: | A class of boundary value problems of fractional differential equations with parameters were studied.Based on the fixed point theorem and the properties of the mixed monotone operator eigenvalue problems,some characteristics of positive solutions to the fractional differential equations depending on the parameters were obtained:existence and uniqueness,monotonicity,continuity and limitations.In the end,an example was given to illustrate the rationality of the main results. |
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| Keywords: | fractional differential equation positive solution existence and uniqueness parameter mixed monotone operator |
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