A reproducing kernel method for solving nonlocal fractional boundary value problems. (English) Zbl 1242.65144

Summary: We propose a reproducing kernel method for solving singular and nonsingular boundary value problems of integer order based on the reproducing kernel theory. In this letter, we expand the application of reproducing kernel theory to fractional differential equations and present an algorithm for solving nonlocal fractional boundary value problems. The results from numerical examples show that the present method is simple and effective.


65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
34A08 Fractional ordinary differential equations
46E22 Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces)
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