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Fractional approach for a mathematical model of atmospheric dynamics of CO2 gas with an efficient method

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  • Ilhan, Esin
  • Veeresha, P.
  • Baskonus, Haci Mehmet

Abstract

In the present work, we find the series solution for the system of fractional differential equations describing the atmospheric dynamics of carbon dioxide (CO2) gas using the q-homotopy analysis transform method (q-HATM). The analyzed model consists of a system of three nonlinear differential equations elucidating the dynamics of human population and forest biomass in the atmosphere to the concentration of CO2 gas. In the current study, we consider Caputo-Fabrizio (CF) fractional operator and the considered scheme is graceful amalgamations of Laplace transform with q-homotopy analysis technique. To present and validate the effectiveness of the hired algorithm, we examined the considered system in terms of fractional order. The existence and uniqueness are demonstrated by using the fixed-point theory. The accomplished consequences illustrate that the considered scheme is highly methodical and very efficient in analyzing the nature of the system of arbitrary order differential equations in daily life.

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  • Ilhan, Esin & Veeresha, P. & Baskonus, Haci Mehmet, 2021. "Fractional approach for a mathematical model of atmospheric dynamics of CO2 gas with an efficient method," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    • Handle: RePEc:eee:chsofr:v:152:y:2021:i:c:s0960077921007013
    DOI: 10.1016/j.chaos.2021.111347
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    1. Dubey, Ved Prakash & Dubey, Sarvesh & Kumar, Devendra & Singh, Jagdev, 2021. "A computational study of fractional model of atmospheric dynamics of carbon dioxide gas," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    2. Jarad, Fahd & Abdeljawad, Thabet & Hammouch, Zakia, 2018. "On a class of ordinary differential equations in the frame of Atangana–Baleanu fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 16-20.
    3. Alexiadis, Alessio, 2007. "Global warming and human activity: A model for studying the potential instability of the carbon dioxide/temperature feedback mechanism," Ecological Modelling, Elsevier, vol. 203(3), pages 243-256.
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    3. Ali, Khalid K. & Wazwaz, Abdul-Majid & Maneea, M., 2024. "Efficient solutions for fractional Tsunami shallow-water mathematical model: A comparative study via semi analytical techniques," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    4. Skwara, Urszula & Mozyrska, Dorota & Aguiar, Maira & Stollenwerk, Nico, 2024. "Dynamics of vector-borne diseases through the lens of systems incorporating fractional-order derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    5. Zulqurnain Sabir & Thongchai Botmart & Muhammad Asif Zahoor Raja & Wajaree Weera, 2022. "An advanced computing scheme for the numerical investigations of an infection-based fractional-order nonlinear prey-predator system," PLOS ONE, Public Library of Science, vol. 17(3), pages 1-13, March.
    6. Stefania Tomasiello & Jorge E. Macías-Díaz, 2023. "A Mini-Review on Recent Fractional Models for Agri-Food Problems," Mathematics, MDPI, vol. 11(10), pages 1-12, May.

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