Chaotic dynamics and stability analysis of the Von Foerster–Lasota PDE with conformable space–time derivatives in Orlicz space

This study rigorously investigates the asymptotic dynamics of systems governed by the space–time conformable Von Foerster–Lasota partial differential equation of order $\kappa \in (0,1)$, where both the temporal and spatial variables are defined in the conformable sense. We establish sufficient conditions for the emergence of Devaney chaos and provide a detailed analysis of the strong stability of the associated solution $\kappa$-semigroup within Orlicz spaces induced by a convex $\mathrm{\Psi }$-function. By employing Matuszewska–Orlicz indices, we offer a precise characterization of the long-term behavior of the generated $\kappa$-semigroup. Notably, this work bridges the gap between the studies of Dawidowicz and Poskrobko (2016), who considered Orlicz spaces for classical derivatives, and Elkhalloufy et al. (2025), who investigated conformable equations in Lebesgue spaces. By extending the conformable framework to the more general setting of Orlicz spaces, we offer new insights into the interplay between chaotic dynamics and stability in structured population models.