  In this article, a new reproducing kernel approach is developed for obtaining
numerical solution of nonlinear three-point boundary value problems with
fractional order. This approach is based on reproducing kernel which is
constructed by shifted Legendre polynomials. In considered problem, fractional
derivatives with respect to $\alpha$ and $\beta$ are defined in Caputo sense.
This method has been applied to some examples which have exact solutions. In
order to shows the robustness of the proposed method, some numerical results
are given in tabulated forms.
