Application of $\left(\frac{G^{\prime}}{G}\right)$-Expansion Method on Conformable Time-Fractional Generalized Burger–Fisher Equation (TF–GBFE)

The time-fractional generalized Burger-Fisher equation (TF-GBFE) is a fractional partial differential equation that combines features of the well-known Burger equation and Fisher equation. By implementing the $\left(\frac{G^{\prime}}{G}\right)$- expansion method, exact solutions for TF-GBFE have been derived. Among the discovered solutions are soliton waves, which are highly significant in nonlinear wave phenomena and are characterised by localised waveforms that keep their shape while propagating. Overall, this study showcases how effective, practical, and accurate is the $\left(\frac{G^{\prime}}{G}\right)$ - expansion method in solving TF-GBFE and emphasizes its potential for the study of other conformable fractional partial differential equations.