Rasekhinezhad, HajarAbbasbandy, SaeidAllahviranloo, TofighBaboliand, Esmail2024-05-192024-05-1920242195-268X2195-2698https://doi.org10.1007/s40435-024-01397-5https://hdl.handle.net/20.500.12713/4855This paper studies the variable fractional functional boundary value problems (VFF-BVPs) by considering Caputo fractional derivative. We use the reproducing kernel method (RKM) without the orthogonalization process as a smart scheme. For this purpose, we construct a reproducing kernel that does not satisfy the boundary condition of VFF-BVP. With this kernel, we can better approximate the solutions for VFF-BVP. Using this method increases the accuracy of the approximate solution so that a significant error analysis can be produced. Finally, two numerical examples are solved to illustrate the efficiency of the present method.eninfo:eu-repo/semantics/closedAccessCaputo Fractional DerivativeVariable FractionalReproducing Kernel MethodBoundary Value ProblemsOrthogonalization ProcessArticleWOS:0011871355000012-s2.0-85188094759N/A10.1007/s40435-024-01397-5Q2