ECCOMAS 2024

Numerical Assessment of Fractional Order Modelling with Applications in Vegetation Pattern Dynamics

  • Ahmad, Zubair (University of Campania, “Luigi Vanvitelli”)
  • Cardone, Angelamaria (University of Salerno)
  • Toraldo, Gerardo (University of Campania, “Luigi Vanvitelli”)
  • Giannino, Francesco (University of Naples Federico II)

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Abstract: Understanding the mechanisms behind vegetation patterns is essential for ecological sustainability and effective resource management. This talk explores the utilization of fractional order modeling to represent more precisely the complex dynamics of vegetation patterns. Fractional order differential equations provide an advanced technique for representing the complex interactions that are essential to ecological systems. The study used a fractional order model to examine the spatial and temporal dynamics of vegetation patterns. Starting from the integer order PDEs model proposed in [1], we propose a time fractional PDEs system. For numerical simulations, this system is then transformed into a system of fractional differential equations, by discretizing the spatial domain with standard techniques. This model is analyzed utilizing advanced computational approaches to get numerical insights. The findings are displayed via different figures, such as 2D and 3D graphs, that show variations in vegetation patterns throughout time. The study covers multiple aspects, such as the influence of the value of the fractional derivation index on pattern formations. The talk ends by examining the effects of utilizing fractional order modeling to improve our knowledge of vegetation dynamics. Information obtained from this research can enhance the development of more efficient approaches for ecological preservation and management of land.