Monotone iterative solutions for nonlinear boundary value problems of fractional differential equation with deviating arguments
Monotone iterative solutions for nonlinear boundary value problems of fractional differential equation with deviating arguments
复制标题
DOI：
10.1155/2013/493164
复制
发表时间：
2013-09
期刊：
影响因子：
--
通讯作者：
Chaozhu Hu;B. Liu;S. Xie
中科院分区：
文献类型：
--
作者：
Chaozhu Hu;B. Liu;S. Xie
利用拟上下解方法和单调迭代技巧，研究了一类具有Caputo分数阶导数的非线性边值问题，引入了两个一致收敛于实际解的单调拟上下解序列，并得到了该问题解的存在性结果.通过一个数值迭代方法得到了精确的近似解，并通过一个算例验证了新方法的精度和效率。
By means of the method of quasi-lower and quasi-upper solutions and monotone iterative technique, we consider the nonlinear boundary value problems with Caputo fractional derivative and introduce two well-defined monotone sequences of quasi-lower and quasi-upper solutions which converge uniformly to the actual solution of the problem, and then the existence results of the solution for the problems are established. A numerical iterative scheme is introduced to obtain an accurate approximate solution and to give one example to demonstrate the accuracy and efficiency of the new approach.