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

作　　者：刘玉记[1] 

机构地区：[1]广东财经大学数学与统计学院,广州510320

出　　处：《数学年刊（A辑）》2014年第6期757-768,共12页Chinese Annals of Mathematics

基　　金：广东省自然科学基金(No.S2011010001900);广东省教育厅高层次人才项目的资助

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.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.

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 

分 类 号：O175.8[理学—数学]