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

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.