Comparison Of Analytical Methods For Solving Fractional Biological Model Via The \((G' / G)\)-Expansion Method

Abstract

This study explores exact traveling wave solutions for a time fractional biological population model by applying the \((G'/G)\)-expansion method. The model, which incorporates nonlinear diffusion and memory effects via fractional derivatives, captures the dynamics of population distribution in a spatially extended biological system. By applying a systematic wave transformation, we reduce the governing partial differential equation to an ordinary differential form and construct a broad class of analytical solutions, including hyperbolic, trigonometric, and rational wave structures. The obtained results not only generalize known solutions from prior literature but also yield novel solution families such as kink, lump, and peakon type waves. Comprehensive symbolic computations using \texttt{Maple} validate the derived expressions, and graphical illustrations demonstrate the physical relevance and diversity of the wave phenomena. The findings highlight the robustness and versatility of the \((G'/G)\)-expansion method for solving complex nonlinear fractional PDEs in biological and ecological modeling.