Numerical Evaluation of Fractional-Order Behaviour in a Nonlinear Climate Forecasting Model for Nigeria Temperature Anomalies Using Atangana-Baleanu Predictor-Corrector

Abstract

Understanding long-term climate variability remains essential for environmental planning and sustainability in developing countries such as Nigeria. This study develops a nonlinear climate forecasting model with fractional-order capability for the simulation and prediction of annual temperature anomalies in Nigeria from 1960 to 2050. Annual temperature anomaly data referenced to the 1961–1990 climatological baseline were obtained from Berkeley Earth, while radiative forcing data were sourced from the Coupled Model Intercomparison Project Phase 6 (CMIP6). The model incorporates external radiative forcing, nonlinear thermal stabilization, and an Atangana–Baleanu fractional derivative framework. Numerical simulations were implemented in MATLAB R2016a using a predictor–corrector algorithm, while model performance was evaluated against Euler, Runge–Kutta fourth-order (RK4), and autoregressive AR(1) approaches using RMSE and coefficient of determination metrics. Parameter estimation yielded a = -0.023822, b = 0.060654, c = 0.072747, and ∝ = 1.00000. The convergence of the fractional order toward unity indicates that the calibrated annual anomaly series behaves predominantly as a classical nonlinear climate system with limited evidence of strong long-memory effects at the national aggregation scale. Sensitivity to fractional order showed ∝<1 unpredicted observed warming, only ∝ =1 tracked the trend.