Analysis of a fractional order climate model due to excessive emission and accumulation of carbon dioxide in the atmosphere

Peter Urane Achimugwu; Mathew Ngugi Kinyanjui; David Mumo Malonza

doi:10.46481/jnsps.2023.1749

Authors

Peter Urane Achimugwu
[email protected]
Pan African University Institute for Basic Sciences, Technology and Innovation, Nairobi, Kenya
Mathew Ngugi Kinyanjui Department of Pure and Applied Mathematics, Jomo Kenyatta University of Agriculture and Technology, Juja, Kenya
David Mumo Malonza Department of Mathematics and Actuarial Science, South Eastern Kenya University, Kitui, Kenya

Keywords:

Climate change, Fractional order, Carbon dioxide, Excessive emission

Abstract

The devastating consequences of climate change on our planet cannot be taken lightly. Greenhouse gas emissions due to the various activities of the increasing human population are solely responsible for this change. The chief and most significant of these gases is carbon dioxide. A fractional-order model of five compartments is considered. The uniqueness and existence, the positivity, and the boundedness of the model solution are established. The equilibrium points of the model are given. By formulating different Lyapunov functions, the global stability of the four equilibrium points was determined. The numerical simulation of the model was done using the Predict-Evaluate-Correct-Evaluate method of Adam-Bashforth-Moulton by considering four different orders of 0.7, 0.8, 0.9, and 1.0. According to the results, excessive concentrations of carbon dioxide in the atmosphere can be reduced by the joint employment of mitigation measures.

Dimensions

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