Sakar, Mehmet GiyasSaldir, Onur2025-05-102025-05-1020202504-311010.3390/fractalfract40400532-s2.0-85097256971https://doi.org/10.3390/fractalfract4040053https://hdl.handle.net/20.500.14720/6855Saldir, Onur/0000-0002-5292-9458; Sakar, Mehmet Giyas/0000-0002-1911-2622In 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.eninfo:eu-repo/semantics/openAccessShifted Legendre PolynomialsReproducing Kernel MethodVariable CoefficientCaputo DerivativeThree-Point Boundary Value ProblemArticle44Q1Q1WOS:000601450900001