论文标题
非线性分数三点边界值问题的新繁殖内核方法
A new reproducing kernel approach for nonlinear fractional three-point boundary value problems
论文作者
论文摘要
在本文中，开发了一种新的复制核方法，用于通过分数顺序获得非线性三点边界值问题的数值解。这种方法基于繁殖核，该核是由转移的Legendre多项式构建的。在被考虑的问题中，在Caputo意义上定义了相对于$α$和$β$的分数衍生物。该方法已应用于具有精确解决方案的一些示例。为了显示所提出方法的鲁棒性，以表格形式给出了一些数值结果。
In this article, a new reproducing kernel approach is developed for obtaining numerical solution of nonlinear three-point boundary value problems with fractional order. This approach is based on reproducing kernel which is constructed by shifted Legendre polynomials. In considered problem, fractional derivatives with respect to $α$ and $β$ are defined in Caputo sense. This method has been applied to some examples which have exact solutions. In order to shows the robustness of the proposed method, some numerical results are given in tabulated forms.
