Numerical methods and their applications in fisheries Science
No Thumbnail Available
Date
2025-06
Authors
Boukhira Oussama
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Mathematicalmodeling plays a crucial role in understanding and predicting the behavior of complex real-world systems. Differential equations, particularly fractional-order models, provide a powerful framework for capturing the dynamics of systems where memory effects and non-local behaviors are significant. This thesis extends a classical predator-prey fishery model by incorporating the Caputo fractional derivative to account for ecological memory effects, which are
essential for realistic predictions in marine population dynamics. The model explores the interactions between prey and predator species distributed across two zones: an open-access fishing area and a protected refuge. The work utilizes the Atangana-Toufik numerical method, a novel approach for solving fractional differential equations, to simulate and analyze the system’s behavior. The results highlight the influence of fractional-order dynamics on population stability,
harvesting strategies, and the resilience of marine ecosystems. This study provides insights into the role of fractional calculus in ecological modeling and offers practical guidance for sustainable fishery management, emphasizing the importance of considering long-term dependencies in decision-making processes.