<p>This paper presents a robust computational technique to tackle the intricate nonlinear partial differential equations (PDEs) encountered in mathematical physics. The method is applied to the time-fractional Burgers-Huxley equation, where the time derivative is considered in the Liouville-Caputo sense. This equation, which combines the well-known Burgers and Huxley equations, describes the interplay of reaction, convection, and diffusion in transport phenomena and finds application in acoustics, turbulence theory, traffic flow, and hydrodynamics. The proposed method transforms this complex non-linear fractional PDE into a simple algebraic system. Its ability to handle the non-linear terms without perturbation, discretization, or the calculation of extraneous terms is a major advantage over available analytical approaches. Five different cases of the equation with diverse initial and boundary conditions are discussed. To demonstrate the accuracy and reliability of the semi-analytic approach, the obtained outcomes are compared with existing exact and analytical solutions in the literature, showing a strong level of agreement. Error analysis and the convergence criterion are also discussed.</p>