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

Khadija Elkhalloufy; Manal Menchih; Khalid Hilal; Ahmed Kajouni; Khadija Elkhalloufy; Manal Menchih; Khalid Hilal; Ahmed Kajouni

doi:10.3934/math.2026276

AIMS Mathematics

2026, Volume 11, Issue 3: 6674-6698. doi: 10.3934/math.2026276

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

Laboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University, Beni Mellal, Morocco

Received: 30 September 2025 Revised: 14 January 2026 Accepted: 02 March 2026 Published: 16 March 2026
MSC : 35B10, 35B35, 35B404

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 $ \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.
- chaos,
- stability,
- conformable derivative,
- $ \kappa $-semigroup,
- Von Foerster Lasota equation,
- Orlicz space,
- Matuszewska-Orlicz indices
Citation: Khadija Elkhalloufy, Manal Menchih, Khalid Hilal, Ahmed Kajouni. Chaotic dynamics and stability analysis of the Von Foerster–Lasota PDE with conformable space–time derivatives in Orlicz space[J]. AIMS Mathematics, 2026, 11(3): 6674-6698. doi: 10.3934/math.2026276

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Abstract

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 $ \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.

References

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