Modeling long-term memory in climate systems through fractional calculus: advancing resilient urban futures at the nexus of innovation and sustainability in Plateau North Central, Plateau state, Nigeria

Abstract

This study introduces a fractional energy balance model (FEBM) utilizing the Caputo fractional derivative to better capture the long-term, cumulative impact of historical climate drivers like greenhouse gas concentrations and radiative forcing. By incorporating memory kernels, the FEBM addresses the limitations of traditional integer-order models that lack memory and fail to accurately model long-term climate persistence. Analytical solutions are derived using Laplace transforms and Mittag-Leffler functions, demonstrating superior ability to simulate delayed and aggregated temperature anomalies. The FEBM provides enhanced predictive power for global surface temperature anomalies, directly supporting robust climate risk management and the development of sustainable, evidence-based urban and health strategies. By leveraging fractional calculus to account for memory and hereditary properties in climate processes, this research advances climate science and exemplifies the synergy between mathematical innovation and sustainability initiatives.