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An algorithm for numerical study of fractional atmospheric model using Bernoulli polynomials

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Abstract

Our paper presents the chaotic behaviour of atmospheric systems with fractional order by using Bernoulli wavelet collocation technique. This technique has not yet been implemented on this model. The study have analysed the dynamics of three climate components—green house gases, temperature and permafrost thaw. To determine the simplicity and efficiency of the developed technique, numerical results have obtained. The combination of graphs and tables shows the stability and efficacy of the developed strategy. Based on the obtained results, we have draw the conclusion that this method offers superior accuracy and efficiency to other methods such as Adam Bashforth’s method, Forward Euler’s method and fde 12 solver method. This study have reveals the effectiveness of the numerical technique as well as the effect of the non integer derivative on atmospheric models. All calculations have been done using a mathematical program called Matlab. Environmental science can be better understood through these studies.

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Data Availibility Statement

Data available on request from the authors.

References

  1. Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations, Vol. 23. Elsevier Science Limited (2006)

  2. Lakshmikantham, V., Leela, S., Devi, J.V.: Theory of Fractional Dynamic Systems. https://books.google.co.in/books?id=5RY8NwAACAAJ (2009)

  3. Magin, R.L.: Fractional calculus models of complex dynamics in biological tissues. Comput. Math. Appl. 59(5), 1586–1593 (2010)

    Article  MathSciNet  Google Scholar 

  4. Hilfer, R.: Applications of Fractional Calculus in Physics. World Scientific (2000)

  5. Naik, M.K., Baishya, C., Veeresha, P., Baleanu, D.: Design of a fractional-order atmospheric model via a class of act-like chaotic system and its sliding mode chaos control. Chaos: Interdiscip. J. Nonlinear Sci. https://doi.org/10.1063/5.0130403 (2023)

  6. Podlubny, I.: Fractional Differential Equations: An Introduction To Fractional Derivatives, Fractional Differential Equations, to Methods of their Solution and Some of their Applications, Vol. 198. Elsevier (1998)

  7. Khan, Z.A., Shah, K., Abdalla, B., Abdeljawad, T.: A numerical study of complex dynamics of a chemostat model under fractal-fractional derivative. Fractals 31(08), 2340181 (2023)

    Article  Google Scholar 

  8. Haq, F., Shah, K., Khan, A., Shahzad, M., et al.: Numerical solution of fractional order epidemic model of a vector born disease by laplace adomian decomposition method. Punjab Univ. J. Math. 49 (2020)

  9. Kumar, R., Kumar, S., Singh, J., Al-Zhour, Z.: A comparative study for fractional chemical kinetics and carbon dioxide CO\(_{2}\) absorbed into phenyl glycidyl ether problems. AIMS Math. 5(4), 3201–3222 (2020)

    Article  MathSciNet  Google Scholar 

  10. Achar, S.J., Baishya, C., Kaabar, M.K.: Dynamics of the worm transmission in wireless sensor network in the framework of fractional derivatives. Math. Methods Appl. Sci. 45(8), 4278–4294 (2022)

    Article  MathSciNet  Google Scholar 

  11. Atangana, A., Baleanu, D.: New fractional derivatives with nonlocal and non-singular kernel: theory and application to heat transfer model. https://doi.org/10.48550/arXiv.1602.03408 (2016)

  12. Yadav, P., Jahan, S., Shah, K., Peter, O.J., Abdeljawad, T.: Fractional-order modelling and analysis of diabetes mellitus: Utilizing the Atangana-Baleanu Caputo (ABC) operator. Alex. Eng. J. 81, 200–209 (2023)

    Article  Google Scholar 

  13. Kneisel, C., Hauck, C., Fortier, R., Moorman, B.: Advances in geophysical methods for permafrost investigations. Permafrost Periglac. Process. 19(2), 157–178 (2008)

    Article  Google Scholar 

  14. Obu, J.: How much of the earth’s surface is underlain by permafrost? J. Geophys. Res. Earth Surface 126 (2021)

  15. Langer, M., von Deimling, T.S., Westermann, S., Rolph, R., Rutte, R., Antonova, S., Rachold, V., Schultz, M., Oehme, A., Grosse, G.: Thawing permafrost poses environmental threat to thousands of sites with legacy industrial contamination. Nat. Commun. 14(1), 1721 (2023)

    Article  Google Scholar 

  16. Pan, Y., Li, L., Jiang, X., Li, G., Zhang, W., Wang, X., Ingersoll, A.P.: Earth changing global atmospheric energy cycle in response to climate change. Nat. Commun. 8(1), 14367 (2017)

    Article  Google Scholar 

  17. Mu, C., Abbott, B., Wu, X., Zhao, Q., Wang, H., Su, H., Wang, S., Gao, T., Guo, H., Peng, X., et al.: Thaw depth determines dissolved organic carbon concentration and biodegradability on the northern qinghai-tibetan plateau. Geophys. Res. Lett. 44(18), 9389–9399 (2017)

    Article  Google Scholar 

  18. Wang, F., Li, Z., Cheng, Y., Li, P., Wang, B., Zhang, H.: Effect of thaw depth on nitrogen and phosphorus loss in runoff of loess slope. Sustainability 14(3), 1560 (2022)

    Article  Google Scholar 

  19. Cui, F., Chen, J., Liu, Z., Zhu, W., Wang, W., Zhang, W.: Prediction model of thermal thawing sensibility and thaw depth for permafrost embankment along the Qinghai-Tibet engineering corridor using modis data. J. Sensors (2020) 1–12

  20. Kumar, A., Kumar, S.: A study on eco-epidemiological model with fractional operators. Chaos Solitons Fract. 156, 111697 (2022)

    Article  MathSciNet  Google Scholar 

  21. Sene, N.: Introduction to the fractional-order chaotic system under fractional operator in Caputo sense. Alex. Eng. J. 60(4), 3997–4014 (2021)

    Article  Google Scholar 

  22. Diouf, M., Sene, N.: Analysis of the financial chaotic model with the fractional derivative operator. Complexity (2020) pp. 1–14

  23. Partohaghighi, M., Veeresha, P., Akgul, A., Inc, M., Riaz, M.B.: Fractional study of a novel hyper-chaotic model involving single non-linearity. Results Phys. 42, 105965 (2022)

    Article  Google Scholar 

  24. Sene, N.: Analysis of a fractional-order chaotic system in the context of the Caputo fractional derivative via bifurcation and lyapunov exponents. J. King Saud Univ.-Sci. 33(1), 101275 (2021)

    Article  Google Scholar 

  25. Sher, M., Shah, K., Sarwar, M., Alqudah, M.A., Abdeljawad, T.: Mathematical analysis of fractional order alcoholism model. Alex. Eng. J. 78, 281–291 (2023)

    Article  Google Scholar 

  26. Shah, K., Abdeljawad, T.: On complex fractal-fractional order mathematical modeling of CO\(_{2}\) emanations from energy sector. Phys. Scr. 99(1), 015226 (2023)

    Article  Google Scholar 

  27. Shiralashetti, S., Mundewadi, R.: Bernoulli wavelet based numerical method for solving Fredholm integral equations of the second kind. J. Inf. Comput. Sci. 11(2), 111–119 (2016)

    Google Scholar 

  28. Chouhan, D., Mishra, V., Srivastava, H.: Bernoulli wavelet method for numerical solution of anomalous infiltration and diffusion modeling by nonlinear fractional differential equations of variable order. Results Appl. Math. 10, 100146 (2021)

    Article  MathSciNet  Google Scholar 

  29. Kumar, S., Ahmadian, A., Kumar, R., Kumar, D., Singh, J., Baleanu, D., Salimi, M.: An efficient numerical method for fractional sir epidemic model of infectious disease by using Bernstein wavelets. Mathematics 8(4), 558 (2020)

    Article  Google Scholar 

  30. Alkahtani, B.S.T., Agrawal, K., Kumar, S., Alzaid, S.S.: Bernoulli polynomial based wavelets method for solving chaotic behaviour of financial model. Results Phys. (2023). https://doi.org/10.1016/j.rinp.2023.107011

    Article  Google Scholar 

  31. Carpinteri, A., Mainardi, F.: Fractals and Fractional Calculus in Continuum Mechanics, Vol. 378. Springer, (2014)

  32. Keshavarz, E., Ordokhani, Y., Razzaghi, M.: Bernoulli wavelet operational matrix of fractional order integration and its applications in solving the fractional order differential equations. Appl. Math. Model. 38(24), 6038–6051 (2014)

    Article  MathSciNet  Google Scholar 

  33. Agrawal, K., Kumar, R., Kumar, S., Hadid, S., Momani, S.: Bernoulli wavelet method for non-linear fractional glucose-insulin regulatory dynamical system. Chaos Solitons Fract. 164, 112632 (2022)

    Article  MathSciNet  Google Scholar 

  34. Moghadam, A.S., Arabameri, M., Baleanu, D., Barfeie, M.: Numerical solution of variable fractional order advection-dispersion equation using Bernoulli wavelet method and new operational matrix of fractional order derivative. Math. Methods Appl. Sci. 43(7), 3936–3953 (2020)

    MathSciNet  Google Scholar 

  35. Noeiaghdam, S., Micula, S., Nieto, J.J.: A novel technique to control the accuracy of a nonlinear fractional order model of covid-19: application of the cestac method and the cadna library. Mathematics 9(12), 1321 (2021)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology, Jamshedpur, Jamshedpur, Jharkhand, 831014, India

    Khushbu Agrawal & Sunil Kumar

  2. Department of Mathematics, Art and Science Faculty Siirt University, 56100, Siirt, Turkey

    Ali Akgül

  3. Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon

    Ali Akgül

Authors
  1. Khushbu Agrawal
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  2. Sunil Kumar
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  3. Ali Akgül
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Correspondence to Khushbu Agrawal.

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Agrawal, K., Kumar, S. & Akgül, A. An algorithm for numerical study of fractional atmospheric model using Bernoulli polynomials. J. Appl. Math. Comput. 70, 3101–3134 (2024). https://doi.org/10.1007/s12190-024-02084-6

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  • DOI: https://doi.org/10.1007/s12190-024-02084-6

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