A new reproducing kernel approach for nonlinear fractional three-point\n boundary value problems

2020/01/09 by Mehmet Giyas Sakar, Sakar, Mehmet Giyas, Onur Saldır +1
Engineering · Mathematics · #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Numerical Analysis (math.NA) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.2001.06357

openalex publication_date 2020/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, a new reproducing kernel approach is developed for obtaining\nnumerical solution of nonlinear three-point boundary value problems with\nfractional order. This approach is based on reproducing kernel which is\nconstructed by shifted Legendre polynomials. In considered problem, fractional\nderivatives with respect to \α and \β are defined in Caputo sense.\nThis method has been applied to some examples which have exact solutions. In\norder to shows the robustness of the proposed method, some numerical results\nare given in tabulated forms.\n

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