Reproducing kernel method to solve non-local fractional boundary value problem

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.

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