10.1007/s40096-021-00418-0

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

  • Raziye Mohammad Hosseiny1,
  • Tofigh Allahviranloo1,
  • Saeid Abbasbandy*2,
  • Esmail Babolian3,
  1. Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, IR
  2. Department of Applied Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, 34149-16818, IR
  3. Computer Science Department, Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, IR

Published in Issue 2021-06-24

How to Cite

Hosseiny, R. M., Allahviranloo, T., Abbasbandy, S., & Babolian, E. (2021). Reproducing kernel method to solve non-local fractional boundary value problem. Mathematical Sciences, 16(3 (September 2022). https://doi.org/10.1007/s40096-021-00418-0
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Abstract

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.

Keywords

  • Fractional differential equations,
  • Non-local boundary value problem,
  • Caputo fractional derivative,
  • Reproducing kernel method,
  • Error analysis

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