In this paper, the weak pre-orthogonal adaptive Fourier decomposition (W-POAFD) method is applied to solve fractional boundary value problems (FBVPs) in the reproducing kernel Hilbert spaces (RKHSs) W04[0,1] and W[0 , 1]. The process of the W-POAFD is as follows: (i) choose a dictionary and implement the pre-orthogonalization to all the dictionary elements; (ii) select points in [0, 1] by the weak maximal selection principle to determine the corresponding orthonormalized dictionary elements iteratively; (iii) express the analytical solution as a linear combination of these determined dictionary elements. Convergence properties of numerical solutions are also discussed. The numerical experiments are carried out to illustrate the accuracy and efficiency of W-POAFD for solving FBVPs.