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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.
65L10Boundary value problems for ODE (numerical methods)
34B05Linear boundary value problems for ODE
34A08Fractional differential equations
46E22Hilbert spaces with reproducing kernels
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