Wavelet-Hermite Fractional Model for Ecological Interactions: for Advancing Climate Modeling and Ecosystem Dynamics

Classical ecological models often overlook memory effects, long-range interactions, and nonlinear dynamics, which are critical under changing climate conditions. Fractional models address these gaps but are frequently limited by computational complexity and instability. To overcome this, we propose a Hermite wavelet operational matrix, offering a fast, stable, and scalable approach for ecological modeling. In this study, we investigate a four-dimensional fractional-order system representing three predator species competing for a single prey, capturing complex ecological dynamics influenced by key biological parameters. Using the Hermite wavelet framework, we solve the model efficiently, even with partially unknown parameters, and validate theoretical outcomes against ecological interpretations. Comparative simulations with the Adam-Bashforth method reveal new chaotic behaviors, while the model’s convergence, boundedness, and uniqueness are established. By examining ecological interactions and their sensitivity to environmental factors, this work supports SDG 13 (Climate Action) and contributes to SDG 14 and 15 by providing tools for sustainable ecosystem management and biodiversity preservation.