A reliable explicit method for time-fractional Benjamin-Bona-Mahony-Burger equation using Pell collocation technique

In this study, a reliable and efficient numerical algorithm based on the Pell collocation method is proposed for solving the time-fractional Benjamin–Bona–Mahony–Burgers (TFBBMB) equation. The fractional derivative in the Caputo sense is employed to capture memory and hereditary effects inherent in complex dynamical systems. By utilizing the operational matrices of Pell polynomials for fractional and integer derivatives, the proposed approach transforms the governing nonlinear fractional partial differential equation into an algebraic system. The convergence and error analyses of the method are rigorously established, proving that the scheme achieves spectral accuracy in both spatial and temporal domains. Several numerical experiments are conducted to verify the stability, efficiency, and accuracy of the presented method. The comparison of the numerical and exact solutions demonstrates excellent agreement and confirms the high precision of the Pell collocation technique compared with existing approaches in the literature.