In this work, an inverse problem of fractional order is considered in which one of the boundary functions is unknown. A finite difference scheme will be proposed to solve numerically the in- verse problem. Due to ill-posedness of this inverse problem, we will employ the mollifcation regularization method with the gen- eralized cross-validation criterion, to find a stable solution. The convergence of numerical scheme is investigated. Finally, a nu- merical example is provided to verify the ability of the proposed method.
