This paper presents a fractional-order modelling framework for population-resource dynamics using the \(\psi\) -Hilfer derivative with neural network-based validation. The model captures logistic population growth coupled to renewable resource biomass while incorporating memory effects through fractional calculus. Novel contributions include the application of the \(\psi\) -Hilfer operator to population-resource systems, representing hereditary dynamics via fractional order \(\zeta\) and type parameter \(\omega\) . A detailed qualitative analysis establishes existence, uniqueness, and Ulam-Hyers (UH) stability with explicit parameter conditions. A linearised quadrature numerical scheme for the \(\psi\) -Hilfer problem is developed and validated through neural networks, achieving \(R^2 \approx 1\) . Simulations reveal that fractional orders ( \(\zeta < 1\) ) produce smoother transients than integer-order counterparts, with \(\zeta\) governing memory strength and \(\omega\) modulating response patterns. Critically, we identify \(E = 150\) as a sustainable harvesting threshold, beyond which resource collapse occurs for integer-order systems, while fractional memory ( \(\zeta = 0.6\) ) provides partial damping. These findings offer actionable policy insights, including optimal harvest limits and stabilisation strategies, advancing both theoretical understanding and practical tools for sustainable resource management.
