A New Reproducing Kernel Approach for Nonlinear Fractional Three-Point Boundary Value Problems

Sakar M. G. , Saldır O.

FRACTAL AND FRACTIONAL, vol.4, no.4, 2020 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 4 Issue: 4
  • Publication Date: 2020
  • Doi Number: 10.3390/fractalfract4040053
  • Journal Name: FRACTAL AND FRACTIONAL
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Keywords: shifted Legendre polynomials, reproducing kernel method, variable coefficient, Caputo derivative, three-point boundary value problem, NUMERICAL-SOLUTION, DIFFERENTIAL-EQUATIONS, ORDER

Abstract

In this article, a new reproducing kernel approach is developed for obtaining a numerical solution of multi-order fractional nonlinear three-point boundary value problems. This approach is based on a reproducing kernel, which is constructed by shifted Legendre polynomials (L-RKM). In the considered problem, fractional derivatives with respect to alpha and beta are defined in the Caputo sense. This method has been applied to some examples that have exact solutions. In order to show the robustness of the proposed method, some examples are solved and numerical results are given in tabulated forms.