Exact Solutions and Dynamic Analysis for a Fractional Partial Differential Equation Emerging in Mathematical Biology

This study investigates a fractional partial differential equation in the field of mathematical biology. The Bernoulli (G'⁄G)-expansion method is applied to solve this class of fractional-order nonlinear differential equations and derive analytical solutions. To illustrate the dynamic properties of the obtained solutions, numerical simulations are conducted, including 3D surface plots, contour maps, and line graphs, highlighting the influence of the beta parameter on solution profiles under specific conditions. Furthermore, dynamical systems theory is employed to examine the equilibrium points of the model, accompanied by corresponding phase portraits. The results confirm the reliability and effectiveness of the Bernoulli (G′/G)-expansion method in handling such nonlinear problems. The ideas presented in this paper can be utilized in a variety of mathematical and physical equations.