Anthropogenic climate change on a non-linear arctic sea-ice model of fractional Duffing oscillator

References

[1] IPCC, “Summary for policymakers,” in IPCC Special Report on the Ocean and Cryospher in a Changing Climate, H. O. Pörtner, D. C. Roberts, V. Masson-Delmotte, et al.., Eds. Geneva, Switzerland, World Meteorological Organization, 2019.Search in Google Scholar

[2] IPCC, “Summary for policymakers,” in Global Warming of 1.5° C. An IPCC Special Report on the Impacts of Global Warming of 1.5° C Above Pre-industrial Levels and Related Global Greenhouse Gas Emission Pathways, in the Context of Strengthening the Global Response to the Threat of Climate Change, Sustainable Development, and Efforts to Eradicate Poverty, V. Masson-Delmotte, P. Zhai, H. O. Pörtner, et al.., Eds., Geneva, Switzerland, World Meteorological Organization, 2018, p. 32.Search in Google Scholar

[3] S. C. Eze and M. O. Oyesanya, “Fractional order on the impact of climate change with dominant earth’s fluctuations,” Math. Clim. Weather Forecast, vol. 5, pp. 1–11, 2019, https://doi.org/10.1515/mcwf-2019-0001.Search in Google Scholar

[4] R. Pierrehumbert, Principals of Planetary Climate, New York, Cambridge University Press, 2010.10.1017/CBO9780511780783Search in Google Scholar

[5] L. A. Trisha, M. Humfrey, and R. Grant Lngram, “Geometrical constructions on the evolution of ridged sea ice,” J. Geophys. Res. Ocean., vol. 109, 2004, https://doi.org/10.1029/2003jc002251.Search in Google Scholar

[6] C. H. Elizabeth, H. L. William, and K. T. Lipscomb, “Sea-ice models for climate study: retrospective and new direction,” J. Glaciol., vol. 56, pp. 1162–1172, 2010, https://doi.org/10.3189/002214311796406096.Search in Google Scholar

[7] D. Grémillet, J. Fort, F. Amélineau, E. Zakharova, T. Le Bot, E. Sala, and M. Gavrilo, “Arctic warming: nonlinear impacts of sea-ice and glacier melt on seabird forcing,” Global Change Biol., vol. 21, no. 3, pp. 1116–1123, 2015, https://doi.org/10.1111/gcb.12811.Search in Google Scholar PubMed

[8] A. Bershadskii, “Nonlinear problems of complex natural systems: sun and climate dynamics,” Phil. Trans. R. Soc. A, p. 20120168, 2013, https://doi.org/10.1098/rsta.2012.0168.Search in Google Scholar PubMed

[9] A. H. Nayfeh and D. T. Mook, Nonlinear Oscillations, London, UK, John Wiley and Sons, 1979.Search in Google Scholar

[10] B. De Saedeleer, M. Crucifix, and S. Wieczorek, “Is the astronomical forcing a reliable and unique pacemaker for climate? A conceptual model study,” Clim. Dynam., vol. 40, pp. 273–294, 2013, https://doi.org/10.1007/s00382-012-1316-1.Search in Google Scholar

[11] S. M. Griffies, “Some ocean model fundamentals,” in Oean Weather Forecasting, E. P. Chassignet and J. Verron, Eds, Dordreecht, Springer, 2006.10.1007/1-4020-4028-8_2Search in Google Scholar

[12] A. Bershadskii, “Subharmonic and chaotic resonances in solar activity,” EPL, vol. 92, p. 50012, 2010, https://doi.org/10.1209/0295-5075/92/50012.Search in Google Scholar

[13] A. M. Raghda, A. M. Attia, L. Dianchen, and M. A Mostafa Khater, “Chaos and relativistic energy-momentum of the nonlinear time fractional duffing equation,” Math. Comput. Appl., vol. 24, p. 10, 2019, https://doi.org/10.3390/mca24010010.Search in Google Scholar

[14] Y. Wang and J. Y. An, “Amplitude-frequency relationship to a fractional duffing oscillator arising in micro-physics and tsunami motion,” J. Low Freq. Noise Vib. Act. Contr., 2018, https://doi.org/10.1177/1461348418795813.Search in Google Scholar

[15] S. M. Tobias and N. O. Weiss, “Resonant interactions between solar activity and climate,” J. Clim., vol. 13, pp. 3745–3754, 2000, https://doi.org/10.1175/1520-0442(2000)013<3745:ribsaa>2.0.co;2.10.1175/1520-0442(2000)013<3745:RIBSAA>2.0.CO;2Search in Google Scholar

[16] S. Minobe and F.-F. Jin, “Generation of interannual and interdecadal climate oscillations through nonlinear subharmonic resonance in delayed oscillators,” Geophys. Res. Lett., vol. 31, p. L16206, 2004, https://doi.org/10.1029/2004GL019776.Search in Google Scholar

[17] J. Brindley, T. Kapitaniak, and A. Barcilon, “Chaos and noisy periodicity in forced ocean atmosphere models,” Phys. Lett. A, vol. 167, pp. 179–184, 1992, https://doi.org/10.1016/0375-9601(92)90225-B.Search in Google Scholar

[18] A. A. M. Arafa, S. Z. Rida, A. A. Mohammadein, and H. M. Ali, “Solving nonlinear fractional differential equation by generalized mittag-leffler function method,” Commun. Theor. Phys., vol. 59, pp. 661–663, 2013, https://doi.org/10.1088/0253-6102/59/6/01.Search in Google Scholar

[19] A. M. A. El-Sayed, S. Z. Rida, and A. A. M. Arafa, “On the solutions of the generalized reaction-diffusion model for bacteria growth,” Acta Appl. Math., vol. 110, pp. 1501–1511, 2010, https://doi.org/10.1007/s10440-009-9523-4.Search in Google Scholar

[20] A. Al-Refai, M. Ali Hajji, and M. I. Syam, “An efficient series solution for fractional differential equations,” Abstr. Appl. Anal., 2014, https://doi.org/10.1155/2014/891837.Search in Google Scholar

[21] S. Z. Rida, A. M. A. El-Sayed, and A. A. M. Arafa, “On the solutions of time-fractional reaction-diffusion equation,” Commun. Nonlinear Sci. Numer. Simulat., vol. 15, pp. 3847–3856, 2010, https://doi.org/10.1016/j.cnsns.2010.02.007.Search in Google Scholar

[22] K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, New York, Wiley, 1993.Search in Google Scholar

[23] K. B. Oldham and J. Spanier, The Fractional Calculus, San Diego, Academic Press, 1974.Search in Google Scholar

[24] J. F. Gómez-Aguilar, R. Razo-Hernández, and D. Granados-Lieberman, “A physical interpretation of fractional calculus in observables terms: analysis of fractional time constant and the transitory response,” Rev. Mexic. Fisica, vol. 60, pp. 32–38, 2014.Search in Google Scholar

[25] I. Petras, Fractional-Order Nonlinear Systems, London, Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg, 2011.10.1007/978-3-642-18101-6Search in Google Scholar

[26] K. Diethelm and N. Ford, “Analysis of fractional differential equations,” J. Math. Anal. Appl., vol. 265, pp. 229–248, 2002, https://doi.org/10.1006/jmaa.2000.7194.Search in Google Scholar

[27] K. Diethelm, Analysis of Fractional Differential Equations, London, Springer-Verlag Berlin Heidelberg, 2010.10.1007/978-3-642-14574-2Search in Google Scholar

[28] C. Yuan, M. Wei-Gang, and M. Lian-Chuan, “Local fractional functional method for solving diffusion equations on cantor sets,” Abstr. Appl. Anal., 2014, https://doi.org/10.1155/2014/803693.Search in Google Scholar

[29] L. M Yang, Y. Han, J. Li, and W. X. Liu, “On steady heat flow problem involving Yang-srivastava-machado fractional derivative without singular kernel,” Therm. Sci., vol. 20, no. 3, pp. 719–723, 2016, https://doi.org/10.2298/tsci16s3717y.Search in Google Scholar

[30] X. J. Yang, H. M. Srivastava, and J. A. T. Machado, “A new fractional derivative without singular kernel: application to the modelling of the steady heat flow,” Therm. Sci., vol. 20, no. 2, pp. 753–756, 2016, https://doi.org/10.2298/tsci151224222y.Search in Google Scholar

[31] F. Gao, “General fractional calculus in non-singular power-law kernel applied to model anomalous diffusion phenomena in heat transfer problems,” Therm. Sci., vol. 21, pp. 11–18, 2017, https://doi.org/10.2298/tsci170310194g.Search in Google Scholar

[32] X. J. Yang, M. Ragulskis, and T. Taha, “A new general fractional-order derivative with Rabotnov fractional-exponential kernel,” Therm. Sci., no. 6B, pp. 254–254, 2019.10.2298/TSCI180825254YSearch in Google Scholar

[33] X. J. Yang, F. Gao, Y. Ju, and H. W. Zhou, “Fundamental solutions of the general fractional-order diffusion equations,” Math. Methods Appl. Sci., vol. 41, no. 18, pp. 9312–9320, 2018, https://doi.org/10.1002/mma.5341.Search in Google Scholar

[34] M. Caputo and M. Fabrizio, “A new definition of fractional derivative without singular kernel,” Progr. Fract. Differ. Appl., vol. 1, no. 2, pp. 1–13, 2015, https://doi.org/10.12785/pfda/010201.Search in Google Scholar

[35] X. J. Yang, D. Baleanu, and H. M. Srivastava, Local Fractional Integral Transforms and Their Applications, Hongkong, Academic Press, 2015.10.1016/B978-0-12-804002-7.00004-8Search in Google Scholar

[36] X. J. Yang and J. T. Machado, “A new fractal nonlinear burgers’ equation arising in the acoustic signals propagation,” Math. Methods Appl. Sci., vol. 42, no. 18, pp. 7539–7544, 2019, https://doi.org/10.1002/mma.5904.Search in Google Scholar

[37] X. J. Yang, Advanced Local Fractional Calculus and its Applications, New York, World Science Publisher, 2012.Search in Google Scholar

[38] X. J. Yang, “Fractional derivatives of constant and variable orders applied to anomalous relaxation models in heat transfer problems,” Therm. Sci., vol. 21, no. 3, pp. 1161–1171, 2016, https://doi.org/10.2298/TSCl161216326Y.Search in Google Scholar

[39] X. J. Yang, General Fractional Derivatives: Theory, Methods and Applications, New York, CRC Press, 2019.10.1201/9780429284083Search in Google Scholar

[40] X. J. Yang, F. Geo, and Y. Ju, General Fractional Derivatives with Applications in Viscoelasticity, Hongkong, Academic Press, 2020.10.1016/B978-0-12-817208-7.00011-XSearch in Google Scholar

[41] S. C. Eze, “Analysis of fractional duffing oscillator,” Rev. Mexic. Fisica, vol. 66, no. 2, pp. 187–191, 2020, https://doi.org/10.31349/revmexfis.66.187.Search in Google Scholar

[42] M. O. Oyesanya, “Stability analysis of fractional duffing oscillator,” Trans. NAMP, vol. 1, pp. 133–150, 2015, 2(2016), 325–342.Search in Google Scholar

[43] B. Saltzman, “A survey of statistical-dynamical models of terrestrial climates,” Adv. Geophys., vol. 20, pp. 281–304, 1978, https://doi.org/10.1016/S0065-2687(08)60324-6.Search in Google Scholar

[44] B. Saltzman and R. E. Moritz, “A time-dependent climate feedback system involving sea-ice extent, ocean temperature and CO2,” Tellus, vol. 32, pp. 93–118, 1980, https://doi.org/10.3402/tellusa.v32i2.10486.Search in Google Scholar

[45] B. Saltzman, A. Sutera, and A. Evenson, “Structural stochastic stability of a simple auto-oscillatory climate feedback system,” J. Atmos. Sci., vol. 38, pp. 494–503, 1981, https://doi.org/10.1175/1520-0469(1981)038<0494:sssoas>2.0.co;2.10.1175/1520-0469(1981)038<0494:SSSOAS>2.0.CO;2Search in Google Scholar

[46] B. Saltzman, “Stochastically-driven climate fluctuations in the sea-ice, ocean temperature, CO2 feedback system,” Tellus, vol. 34, pp. 97–112, 1981, https://doi.org/10.1111/j.2153-3490.1982.tb01797.x.Search in Google Scholar

[47] B. Saltzman, A. Sutera, and A. Hansen, “A possible marine mechanism for internally generated long-period climate cycles,” J. Atmos. Sci., vol. 39, pp. 2634–2637, 1982, https://doi.org/10.1175/1520-0469 039<2634:APMMFI>2.0.CO;2.10.1175/1520-0469(1982)039<2634:APMMFI>2.0.CO;2Search in Google Scholar

[48] J. Brindley, T. Kapitaniak, and A. Barcilon, “Chaos and noisy periodicity in forced ocean atmosphere models,” Phys. Lett. A, vol. 167, pp. 179–184, 1992, https://doi.org/10.1016/0375-9601(92)90225-B.Search in Google Scholar

[49] G.T. Farmer and J. Cook, Climate Change Science: A Modern Synthesis, vol. 1, The Physical Climate, Dordrecht: Springer, 2013.10.1007/978-94-007-5757-8Search in Google Scholar

[50] H. Hermann, “Radiation transfer calculations and assessment of global warming by CO2,” Int. J. Atmos. Sci., 2017, https://doi.org/10.1155/2017/9251034.Search in Google Scholar

[51] P. M. D. Forster and J. M. Gregory, “The climate sensitivity and its components diagnosed from Earth radiation budget data,” J. Clim., vol. 19, pp. 39–52, 2006, https://doi.org/10.1175/jcli3611.1.Search in Google Scholar

[52] IPCC, Climate Change 2007. The Physical Science Basis, Contribution of Working Group I to the Fourth Assessment Report of the IPCC, S. Solomon, D. Qin, M. Manning, Z. Chen, M. Marquis, K. B. Averyt, et al.., Eds. Cambridge, Cambridge University Press, 2007.Search in Google Scholar

[53] J. F. Gómez-Aguilar, J. J. Rosales-García, J. J. Bernal-Alvarado, T. Córdova-Fraga, and R. Guzmán-Cabrera, “Fractional mechanical oscillators,” Rev. Mex. Fis., vol. 58, pp. 348–352, 2012.Search in Google Scholar

[54] R. F. Keeling, S. C. Piper, A. F. Bollenbacher, and J. S. Walker, “Atmospheric CO2 records from sites in the SIO air sampling network,” in Trends: A Compendium of Data on Global Change. Carbon Dioxide Information Analysis Center, Oak Ridge, Tenn., U.S.A, Oak Ridge National Laboratory, U.S. Department of Energy, 2009, https://doi.org/10.3334/CDIAC/atg.035.Search in Google Scholar