This study investigates nonlinear wave propagation in atime-fractional Fisher - Kolmogorov - Petrovskiĭ - Piskunov (Fisher - KPP) - type reaction - diffusion equation that models anomalous diffusion and memory-dependent reaction mechanisms in complex media. The fractional time derivative of order Formula: see text is introduced to represent hereditary effects and subdiffusive transport that lie beyond the scope of classical integer-order Fisher - KPP formulations. By employing the Khater II method as a computational scheme, a family of exact wave-type solutions is derived in closed form, with the fractional order a explicitly shaping the amplitude, spatial width, and propagation characteristics of the resulting fronts. The analysis shows that variations in a systematically modulate front steepness, propagation speed, and relaxation behavior, thereby revealing a smooth transition from classical diffusive profiles to strongly nonlocal, memory-dominated regimes. A stability study, carried out within a Hamiltonian-inspired framework, identifies parameter ranges for the fractional order and reaction strength in which the obtained waves remain dynamically robust under small perturbations. Overall, the results demonstrate that incorporating fractional dynamics into Fisher-KPP-type models produces richer traveling-wave structures and yields a more accurate representation of transport and growth in heterogeneous or porous environments.
Suleman H. Alfalqi (Tue,) studied this question.