SOLITON SOLUTIONS AND CHAOTIC REGIMES: AN ANALYTICAL STUDY OF THE FRACTIONAL FKPP EQUATION

This work investigates the dynamical behavior of the fractional Fisher–Kolmogorov–Petrovsky–Piskunov equation. The model under consideration has significant implications for reaction–diffusion processes and mathematical physics. By use of the wave transform with the [Formula: see text]-fractional derivative, the nonlinear ordinary differential equation of the governing model is extracted. The advanced approaches such as the modified F-expansion method, the modified generalized Riccati equation technique, and the modified generalized exponential rational function technique are utilized to study the model. It comprises numerous types of different solutions such as mixed, dark, bright–dark, singular, bright, complex, combined solitons, hyperbolic, periodic, and exponential solutions. We examine a comprehensive chaotic analysis to examine in depth at how the system behaves in a nonlinear way. This shows how sensitive it is to initial conditions and how strange attractors arise in phase space. Using different parameter selections, the behavior of the solutions is shown in three-dimensional, two-dimensional, and their related contour representations. By validating the effectiveness of current methodologies and elucidating the nonlinear dynamic characteristics of the proposed model, this work substantially advances the disciplines of higher-dimensional nonlinear wave fields and nonlinear science. The results of this study will help identify and elucidate numerous innovative soliton solutions. These solutions are expected to be of great significance in the fields of mathematical physics and other areas of nonlinear science.