This study introduces a novel two-dimensional fractional pseudo-telegraph equation that combines Caputo and Atangana-Baleanu-Caputo (ABC) fractional derivatives—a hybrid approach not previously explored for this class of problems. A finite difference scheme is developed to solve the equation numerically. The stability of the proposed scheme is rigorously established through Von-Neumann analysis, yielding a sufficient stability condition. The convergence order of the method is shown to be $O(\tau^{2-\alpha}+h^2)$, where \(\tau\) and \(h\) denote the temporal and spatial step sizes, respectively. Numerical experiments are conducted for two test problems with known exact solutions. The computed maximum norm errors and CPU times, presented for various grid resolutions, demonstrate that the errors decrease monotonically as the mesh is refined, thereby confirming the accuracy and convergence of the method. The results validate that the proposed hybrid fractional model provides a reliable and efficient computational framework for handling mixed fractional-order derivatives in engineering and physical applications.