In this study, we investigate a two-point boundary value problem involving fractional derivatives (in Caputo sense) of different orders. To address this problem, we employ a finite difference scheme on a uniform mesh, where the fractional derivative of order \(\alpha \in (0,1)\) is approximated using the L1 scheme, while the derivative of order \(\beta \in (1,2)\) is discretized using an explicit finite difference approximation. A rigorous analysis is carried out to establish the invertibility of the resulting discrete system and to derive theoretical error estimates for the proposed scheme. Numerical experiments are performed to assess its performance, indicating a linear rate of convergence consistent with the theoretical results. To further enhance accuracy, Richardson extrapolation is applied. In addition, the model is extended to incorporate nonlocal boundary conditions, and a corresponding numerical scheme is developed along with numerical experiment.
