Computational analysis of Caputo-Fabrizio fractional order climate change model

In this article, we study a Caputo-Fabrizio fractional-order climate model to capture the intrinsic nonlocal and fading-memory characteristics of coupled environmental processes. The framework incorporates five interacting state variables surface temperature T(t), atmospheric carbon concentration C(t), ice fraction I(t), atmospheric activity A(t), and oceanic carbon uptake O(t). The non-singular exponential kernel embedded in the Caputo-Fabrizio operator ensures smooth temporal weighting and realistic climate inertia without introducing singular behavior. Theoretical analysis establishes existence, uniqueness, and dynamical stability of the proposed system within a fractional framework. For computational investigation, we perform numerical analysis using a Fractional Weighted Discrete Iterative Scheme (FWDS), which preserves the exponential memory structure while enabling stable and efficient time-marching of the nonlinear coupled model. Furthermore, an artificial neural network trained via the Levenberg-Marquardt optimization algorithm is employed to learn complex climate interactions and validate numerical accuracy. Strong agreement between analytical findings, discrete simulations, and intelligent predictions demonstrates that integrating fractional calculus with advanced numerical and learning strategies provides a robust and forward-looking framework for long-term climate forecasting and environmental risk assessment. Keyoutput