Existence, Uniqueness and Stability Analysis of a Fractional Stochastic Climate-Carbon-Ecosystem Model with Caputo-Fabrizio Operator

Existence, Uniqueness and Stability Analysis of a Fractional Stochastic Climate-Carbon-Ecosystem Model with Caputo-Fabrizio Operator

Existence, Uniqueness and Stability Analysis of a Fractional Stochastic Climate-Carbon-Ecosystem Model with Caputo-Fabrizio Operator

^1*MKPEDEM K. A; ²FADEPO J. T; ³OLAYIWOLA R.O
¹Department of Mathematics, University of Abuja, Abuja, Nigeria
²Department of Industrial Mathematics, Federal University of Science and Technology, Minna. Niger State, Nigeria
³Department of Industrial Mathematics, Federal University of Science and Technology, Minna. Niger State, Nigeria
^*kufremkpedem@gmail.com, fadepoj@gmail.com, Olayiwola.rssaq@futminna.edu.ng.

Abstract

This paper presents existence, uniqueness and stability analysis of a fractional stochastic climate–carbon–ecosystem model formulated using the Caputo–Fabrizio fractional derivative to incorporate memory effects and stochastic environmental variability in climate dynamics. The model describes the interactions among atmospheric carbon concentration, global temperature anomaly, ecosystem biomass, and mitigation effort through a system of coupled nonlinear fractional differential equations. Using an appropriate Banach space framework, the governing system is transformed into an equivalent integral equation. Sufficient conditions for the existence and uniqueness of solutions are established using fixed-point theory and the Banach contraction principle. Furthermore, local and global stability analyses of the equilibrium states are investigated using Jacobian matrix theory and Lyapunov methods for fractional systems. The results establish the well-posedness and asymptotic stability of the proposed model under suitable assumptions. The study demonstrates that the Caputo–Fabrizio operator provides a mathematically consistent framework for analyzing climate–ecosystem interactions with memory and stochastic effects.

Keywords: Fractional differential equations; Caputo–Fabrizio operator; existence and uniqueness; Banach fixed-point theorem; climate modelling; stochastic systems

DOI: https://doi.org/10.46654/erj.v2n12.2124