OICC Press Mathematical Sciences 2251-7456 16 3 (September 2022) 2021 06 24 Reproducing kernel method to solve non-local fractional boundary value problem 10.1007/s40096-021-00418-0 EN Raziye Mohammad Hosseiny Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, IR Tofigh Allahviranloo Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, IR Saeid Abbasbandy Department of Applied Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, 34149-16818, IR Esmail Babolian Computer Science Department, Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, IR Journal Article 2021 06 24 Abstract 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.