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    Applications of new smart algorithm based on kernel method for variable fractional functional boundary value problems
    (Springernature, 2024) Rasekhinezhad, Hajar; Abbasbandy, Saeid; Allahviranloo, Tofigh; Baboliand, Esmail
    This 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.