Chaotic dynamics and strong stability of conformable von Foerster partial differential equation in Lebesgue space

In this paper, we investigate the chaotic behavior and strong stability of the conformable von Foerster equation of order [Formula: see text]. By analyzing the spectral properties of the [Formula: see text]-infinitesimal generator, we establish the conditions for chaos in the space [Formula: see text] for constant growth rate function, and extend these results to non-constant growth rate function using the concept of conjugacy. We justify the use of the conformable derivative in this context, explaining its relevance for modeling anomalous diffusion and dynamic systems. Additionally, we interpret the obtained conditions in biological terms, linking them to cellular growth regulation and population dynamics. Our results provide novel insights into the dynamics of structured population models and contribute to the study of chaos and stability in conformable partial differential equations.