This paper presents a numerical scheme to solve non-local fractional boundary value problems (NFBVPs) through a different implementation of the general form of the reproducing kernel method (RKM) similar to the method eliminating the Gram–Schmidt orthogonalization process to reduce the CPU time. The presented method provides a reliable technique to obtain a reproducing kernel applicable to non-local conditions of the fractional boundary value problems with the aim of increasing the accuracy of the approximate solutions. Therefore, it would be possible to provide a valid error analysis for NFBVP and the presented method. The accuracy of theoretical results is illustrated by solving two numerical examples.

本文提出了一种数值方案，通过与消除 Gram-Schmidt 正交化过程以减少 CPU 时间的方法类似的再现核方法 (RKM) 的一般形式的不同实现来解决非局部小数边值问题 (NFBVP)。 . 所提出的方法提供了一种可靠的技术来获得适用于分数边值问题的非局部条件的再现核，目的是提高近似解的精度。因此，有可能为 NFBVP 和所提出的方法提供有效的错误分析。通过求解两个数值例子说明了理论结果的准确性。