A Fractional Population Resource Model for Sustainable Development: A Case Study of Maharashtra

Akashay P. Savant,   Dayanand K. Vyavahare

Department of General Science

SKN Singhad College of Engineering, Korti, Pandharpur

Abstract: Sustainable development requires a balanced relationship between population growth and the availability of renewable resources. Classical population models explain growth based on carrying capacity, yet modern socio-ecological systems demonstrate memory effects, delayed feedback, and nonlinear resource dynamics that traditional models fail to capture. To address this, we propose a modified fractional population–resource model that incorporates long-term memory behavior along with the influence of technological efficiency and environmental degradation on resource sustainability. Fractional-order derivatives are applied to represent historical dependence in both population expansion and renewable resource regeneration. The Homotopy Perturbation Method is used to obtain semi-analytical solutions to the governing fractional differential equations. Maharashtra’s demographic data is adopted as a real case study to demonstrate the application of the model to a developing region with high population density and increasing resource demand. The analytical and numerical results highlight the significant role of technology adoption in enhancing resource productivity and slowing population pressure on the environment. At the same time, environmental deterioration is shown to reduce long-term resource availability and threaten the stability of the system. The proposed fractional modeling approach offers a more realistic and flexible framework for examining sustainable population-resource interactions and informing policy planning for long-term development.

Keywords: fractional model, sustainable development, population dynamics, Maharashtra, HPM, resource management.