An iterative shooting-like method based on the shifted Chebyshev polynomials is proposed for solving the nonlinear fractional boundary value problems with the multi-point boundary conditions. The proposed method can be applied easily to various nonlocal linear boundary conditions. Here, we investigate the convergence of the proposed method for the nonlinear problems with the multi-point boundary condition. The obtained numerical results confirm the theoretical results and show the efficiency and accuracy of the proposed method.
