Implementing Bernstein Operational Matrices to Solve a Fractional-Order Smoking Epidemic Model

This paper leverages the Bernstein operational matrices method for the first time in order to resolve the nonlinear fractional smoking epidemic model presented in terms of Caputo’s fractional derivative. An approximate solution is derived using Bernstein’s operational matrices and strategically chosen collocation points. This is followed by the validation of the proposed method’s accuracy and reliability against the established Runge–Kutta fourth-order method. Furthermore, a comprehensive comparative analysis is conducted against two prominent techniques: the fractional differential transform method (FDTM) and the q-homotopy analysis transform method (q-HATM). The results show a superior and significant performance regarding accuracy as well as approximation. A residual corrected error technique is employed to enhance the precision of the presented method, thus effectively minimising absolute errors.