| 刘玉记.半直线上Riemann-Liouville型奇异分数阶微分方程边值问题的单调迭代方法[J].数学年刊A辑,2014,35(6):757~ |
| 半直线上Riemann-Liouville型奇异分数阶微分方程边值问题的单调迭代方法 |
| Monotone Iterative Technique for Singular Boundary Value Problems of Riemann-Liouville Fractional Differential Equations on a Half Line |
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| DOI： |
| 中文关键词: Riemann-Liouville型导数, 奇异分数阶微分方程, 边值问题, Schauder不动点定理, 正解, 单调迭代方法 |
| 英文关键词:Riemann-Liouville derivative, Singular fractional
differential equation, Boundary value problem,
Schauder fixed point theorem, Positive solution, Monotone iterative
technique |
| 基金项目:广东省自然科学基金 (No.S2011010001900) 和
广东省教育厅高层次人才项目 |
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| 中文摘要: |
| 运用不动点定理和单调迭代方法研究半直线上Riemann-Liouville型奇异分数阶微分方程边值问题的正解的存在性.
在没有上、下解存在的假设下建立了边值问题存在两个正解的结果, 构造了逼近正解的迭代格式, 该迭代格式便于应用. |
| 英文摘要: |
| This paper deals with the existence of positive solutions to some
boundary value problems of singular Riemann-Liouville fractional differential equations on half lines.
The approach is based on the fixed point theorem and the monotone
iterative technique. Without the assumption of the existence of
lower and upper solutions, the author obtains not only the existence of
positive solutions to the problems, but also establishes iterative
schemes for approximating the solutions. These schemes are useful
to computation purpose. |
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