A numerical approach to the coupled atmospheric ocean model using a fractional operator

Pundikala VEERASHA (Center for Mathematical Needs, Department of Mathematics, CHRIST (Deemed to be University), Bengaluru-560029, India)
Mathematical Modelling and Numerical Simulation with Applications
3 0
Yıl: 2021 Cilt: 1 Sayı: 1 Sayfa Aralığı: 1 - 10 Metin Dili: İngilizce DOI: 10.53391/mmnsa.2021.01.001 İndeks Tarihi: 21-02-2023

A numerical approach to the coupled atmospheric ocean model using a fractional operator

Öz:
In the present framework, the coupled mathematical model of the atmosphere-ocean system called El Nino-Southern Oscillation (ENSO) is analyzed with the aid Adams-Bashforth numerical scheme. The fundamental aim of the present work is to demonstrate the chaotic behaviour of the coupled fractional-order system. The existence and uniqueness are demonstrated within the frame of the fixed-point hypothesis with the Caputo--Fabrizio fractional operator. Moreover, we captured the chaotic behaviour for the attained results with diverse order. The effect of the perturbation parameter and others associated with the model is captured. The obtained results elucidate that, the present study helps to understand the importance of fractional order and also initial conditions for the nonlinear models to analyze and capture the corresponding consequence of the fractional-order dynamical systems.
Anahtar Kelime:

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
  • [1] M. Caputo, Elasticita e Dissipazione, Zanichelli, Bologna, (1969).
  • [2] K. S. Miller, B. Ross, An introduction to fractional calculus and fractional differential equations, A Wiley, New York, (1993).
  • [3] I. Podlubny, Fractional Differential Equations, Academic Press, New York, (1999).
  • [4] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, Elsevier, Amsterdam, (2006).
  • [5] D. Baleanu, Z.B. Guvenc, J.A. Tenreiro Machado, New trends in nanotechnology and fractional calculus applications, Springer Dordrecht Heidelberg, London New York, (2010).
  • [6] M. Caputo, M. Fabrizio, A new definition of fractional derivative without singular kernel, Progr. Fract. Diff. Appl., 1 (2) (2015), 73-85.
  • [7] K. M. Safare, et.al., A mathematical analysis of ongoing outbreak COVID-19 in India through nonsingular derivative, Numer- ical Methods for Partial Differential Equations 37 (2) (2021), 1282-1298.
  • [8] M. Yavuz, European option pricing models described by fractional operators with classical and generalized Mittag-Leffler kernels, Numerical Methods for Partial Differential Equations, (2021), DOI: 10.1002/num.22645.
  • [9] L. Akinyemi, M. Şenol, S. N. Huseen, Modified homotopy methods for generalized fractional perturbed Zakharov–Kuznetsov equation in dusty plasma, Adv. Differ. Equ., 45 (2021), DOI: 10.1186/s13662-020-03208-5.
  • [10] C. Baishya, S. J. Achar, P. Veeresha, D. G. Prakasha, Dynamics of a fractional epidemiological model with disease infection in both the populations, Chaos, 31 (2021), DOI: 10.1063/5.0028905.
  • [11] J. Fei-Fei, An equatorial ocean recharge paradigm for ENSO. Part I: conceptual model, J. Atmos. Sci., 54 (7) (1996), 811-829.
  • [12] Y. Zen, The Laplace-Adomian-Pade technique for the ENSO model, Math. Probl. Eng, 4 (2013), DOI:10.1155/2013/954857.
  • [13] J. Q. Mo, W. T. Lin, J. Zhu, The variational iteration solving method for El Nino/La Nino-Southern Oscillation model, Adv. Math., 35 (2) (2006), 232–236.
  • [14] J. Q. Mo, W. T. Lin, Generalized variation iteration solution of an atmosphere-ocean oscillator model for global climate, J. Syst. Sci. Complex, 24 (2) (2011), 271-276.
  • [15] Z. Xian-Chun, L. Yi-Hua, W. T. Lin, J. Q. Mo, Homotopic mapping solution of an oscillator for the El nino/La Nina-Southern Oscillation, Chin. Phys. B, 18 (11) (2009), 4603-4605.
  • [16] J. Singh, D. Kumar, J. J. Nieto, Analysis of an El Nino-Southern Oscillation model with a new fractional derivative, Chaos Solitons Fractals, 99 (2017), 109-115.
  • [17] M. Gubes, H. A. Peker, G. Oturanc, Application of differential transform method for El Nino Southern Oscillation (ENSO) model with compared Adomian decomposition and variational iteration methods. J. Math. Comput. Sci., 15 (2015), 167–178.
  • [18] J. Q. Mo JQ, W. T. Lin, Perturbed solution for the ENSO nonlinear model, Acta Phys. Sinica., 53 (4) (2004), 996-998.
  • [19] L. Akinyemi, O.S. Iyiola, A reliable technique to study nonlinear time-fractional coupled Korteweg-de Vries equations, Adv. Differ. Equ., 2020 (2020), 1-27, DOI: 10.1186/s13662-020-02625-w.
  • [20] E. K. Akgül, A. Akgül, M. Yavuz, New Illustrative Applications of Integral Transforms to Financial Models with Different Fractional Derivatives, Chaos Solitons Fractals 146 (2021), 110877.
  • [21] P. Veeresha, E. Ilhan, H. M. Baskonus, Fractional approach for analysis of the model describing wind- influenced projectile motion, Phys. Scr., 96 (2021), DOI: 10.1088/1402-4896/abf868.
  • [22] L. Akinyemi, A fractional analysis of Noyes–Field model for the nonlinear Belousov–Zhabotinsky reaction, Comp. Appl. Math., 39 (2020), 1-34, DOI: 10.1007/s40314-020-01212-9.
  • [23] P. Veeresha, D. G. Prakasha, A reliable analytical technique for fractional Caudrey-Dodd-Gibbon equation with Mittag-Leffler kernel, Nonlinear Eng., 9 (1) (2020), 319–328.
  • [24] M. Yavuz, N. Sene, Fundamental calculus of the fractional derivative defined with Rabotnov exponential kernel and applica- tion to nonlinear dispersive wave model, J. Ocean Eng. Sci., 6 (2) (2021), 196-205.
  • [25] S.-W. Yao, E. Ilhan, P. Veeresha, H. M. Baskonus, A powerful iterative approach for quintic complex Ginzburg-Landau equation within the frame of fractional operator, Fractals, (2021), DOI: 10.1142/S0218348X21400235.
  • [26] L. Akinyemi, P. Veeresha, M. Senol, Numerical solutions for coupled nonlinear Schrodinger-Korteweg-de Vries and Maccari’s systems of equations, Modern Physics Letters B, (2021), 2150339, DOI: 10.1142/S0217984921503395.
  • [27] A. Atangana, R. T. Alqahtani, Numerical approximation of the space-time Caputo–Fabrizio fractional derivative and applica- tion to groundwater pollution equation, Adv. Diff. Equ., 1 (2016), 1–13.
  • [28] C. Baishya, Dynamics of a Fractional Stage Structured Predator-Prey model with Prey Refuge, Indian J. Ecol., 47 (4) (2020), 1118-1124.
  • [29] P. Veeresha, D.G. Prakasha, H.M. Baskonus, New numerical surfaces to the mathematical model of cancer chemotherapy effect in Caputo fractional derivatives, Chaos 29 (013119) (2019). DOI: 10.1063/1.5074099.
  • [30] K. M. Owolabi, A. Atangana, Analysis and application of new fractional Adams–Bashforth scheme with Caputo–Fabrizio derivative, Chaos, Solitons Fractals, 105 (2017), 111–119.
  • [31] A. Atangana, Derivative with a new parameter: theory, methods and applications, New York: Academic Press; 2016.
  • [32] A. Atangana, K. M. Owolabi, New numerical approach for fractional differential equations, Math. Model. Nat. Phenom., 13 (2018), DOI: 10.1051/mmnp/2018010.
  • [33] A. Atangana, J. J. Nieto, Numerical solution for the model of RLC circuit via the fractional derivative without singular kernel, Adv. Mech. Eng., 7(2015), 1–6.
  • [34] M. Caputo, M. Fabrizio, Applications of new time and spatial fractional derivatives with exponential kernels, Progr. Fract. Diff. Appl., 2 (2016), 1–11.
  • [35] J. Losada, J. J. Nieto, Properties of the new fractional derivative without singular kernel, Progr. Fract. Differ. Appl., 1 (2015), 87-92.
  • [36] J. Danane, K. Allali, Z. Hammouch, Mathematical analysis of a fractional differential model of HBV infection with antibody immune response, Chaos Solitons Fractals, 136 (2020).
  • [37] K. M. Owolabi, Z. Hammouch, Spatiotemporal patterns in the Belousov–Zhabotinskii reaction systems with Atan- gana–Baleanu fractional order derivative, Phys. A, 523 (2019), 1072-1090.
  • [38] F. Haq, I. Mahariq, T. Abdeljawad, N. Maliki, A new approach for the qualitative study of vector born disease using Ca- puto–Fabrizio derivative, Numer. Methods Partial Differ. Equ., 37 (2) (2021), 1809-1818.
  • [39] P. Veeresha, H. M. Baskonus, W. Gao, Strong interacting internal waves in rotating ocean: Novel fractional approach, Axioms, 10 (2) (2021).
  • [40] W. Zhong, L. Wang, T. Abdeljawad, Separation and stability of solutions to nonlinear systems involving Caputo–Fabrizio derivatives, Adv. Differ. Equ., 166 (2020). DOI: 10.1186/s13662-020-02632-x.
  • [41] R. Gul, M. Sarwar, K. Shah, T. Abdeljawad, F. Jarad, Qualitative Analysis of Implicit Dirichlet Boundary Value Problem for Caputo-Fabrizio Fractional Differential Equations, J. Funct. Spaces, (2020), DOI: 10.1155/2020/4714032.
  • [42] M. Yavuz, E. Bonyah, New approaches to the fractional dynamics of schistosomiasis disease model, Phys. A, 525 (2019), 373-393.
  • [43] P. Veeresha, D. G. Prakasha, Z. Hammouch, An efficient approach for the model of thrombin receptor activation mechanism with Mittag-Leffler function, Nonlinear Analysis: Problems, Applications and Computational Methods, (2020), 44-60.
  • [44] K. Shah, F. Jarad, T. Abdeljawad, On a nonlinear fractional order model of dengue fever disease under Caputo-Fabrizio derivative, Alexandria Eng. J., 59 (4) (2020), 2305-2313.
  • [45] M. Yavuz, N. Sene, Fundamental calculus of the fractional derivative defined with Rabotnov exponential kernel and applica- tion to nonlinear dispersive wave model, J. Ocean Eng. Sci., 6 (2) (2021), 196-205.
APA Veeresha D (2021). A numerical approach to the coupled atmospheric ocean model using a fractional operator. , 1 - 10. 10.53391/mmnsa.2021.01.001
Chicago Veeresha Dr. P. A numerical approach to the coupled atmospheric ocean model using a fractional operator. (2021): 1 - 10. 10.53391/mmnsa.2021.01.001
MLA Veeresha Dr. P. A numerical approach to the coupled atmospheric ocean model using a fractional operator. , 2021, ss.1 - 10. 10.53391/mmnsa.2021.01.001
AMA Veeresha D A numerical approach to the coupled atmospheric ocean model using a fractional operator. . 2021; 1 - 10. 10.53391/mmnsa.2021.01.001
Vancouver Veeresha D A numerical approach to the coupled atmospheric ocean model using a fractional operator. . 2021; 1 - 10. 10.53391/mmnsa.2021.01.001
IEEE Veeresha D "A numerical approach to the coupled atmospheric ocean model using a fractional operator." , ss.1 - 10, 2021. 10.53391/mmnsa.2021.01.001
ISNAD Veeresha, Dr. P.. "A numerical approach to the coupled atmospheric ocean model using a fractional operator". (2021), 1-10. https://doi.org/10.53391/mmnsa.2021.01.001
APA Veeresha D (2021). A numerical approach to the coupled atmospheric ocean model using a fractional operator. Mathematical Modelling and Numerical Simulation with Applications, 1(1), 1 - 10. 10.53391/mmnsa.2021.01.001
Chicago Veeresha Dr. P. A numerical approach to the coupled atmospheric ocean model using a fractional operator. Mathematical Modelling and Numerical Simulation with Applications 1, no.1 (2021): 1 - 10. 10.53391/mmnsa.2021.01.001
MLA Veeresha Dr. P. A numerical approach to the coupled atmospheric ocean model using a fractional operator. Mathematical Modelling and Numerical Simulation with Applications, vol.1, no.1, 2021, ss.1 - 10. 10.53391/mmnsa.2021.01.001
AMA Veeresha D A numerical approach to the coupled atmospheric ocean model using a fractional operator. Mathematical Modelling and Numerical Simulation with Applications. 2021; 1(1): 1 - 10. 10.53391/mmnsa.2021.01.001
Vancouver Veeresha D A numerical approach to the coupled atmospheric ocean model using a fractional operator. Mathematical Modelling and Numerical Simulation with Applications. 2021; 1(1): 1 - 10. 10.53391/mmnsa.2021.01.001
IEEE Veeresha D "A numerical approach to the coupled atmospheric ocean model using a fractional operator." Mathematical Modelling and Numerical Simulation with Applications, 1, ss.1 - 10, 2021. 10.53391/mmnsa.2021.01.001
ISNAD Veeresha, Dr. P.. "A numerical approach to the coupled atmospheric ocean model using a fractional operator". Mathematical Modelling and Numerical Simulation with Applications 1/1 (2021), 1-10. https://doi.org/10.53391/mmnsa.2021.01.001
Sayfa Oluşturulma Tarihi
24-04-2024 2:22

İLETİŞİM

TÜBİTAK ULAKBİM TR Dizin

Yüzüncüyıl, İşçi Blokları Mahallesi

Muhsin Yazıcıoğlu Caddesi No:51/C

06530 Çankaya / ANKARA +90 (312) 298 92 00

trdizin@tubitak.gov.tr

TÜBİTAK ULAKBİM Ulusal Akademik Ağ ve Bilgi Merkezi Cahit Arf Bilgi Merkezi © Tüm Hakları Saklıdır. Gizlilik Politikası Kullanım Şartları