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A new iterative technique for a fractional model of nonlinear Zakharov–Kuznetsov equations via Sumudu transform

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  • Prakash, Amit
  • Kumar, Manoj
  • Baleanu, Dumitru

Abstract

The main objective of this paper is to suggest a new computational technique namely new iterative Sumudu transform method (NISTM) to solve numerically nonlinear time-fractional Zakharov–Kuznetsov (FZK) equation in two dimensions. We implemented the proposed technique on two test examples, plotted the solution and compared the absolute error with the variational iterative technique (VIM) and homotopy perturbation transform method (HPTM).

Suggested Citation

  • Prakash, Amit & Kumar, Manoj & Baleanu, Dumitru, 2018. "A new iterative technique for a fractional model of nonlinear Zakharov–Kuznetsov equations via Sumudu transform," Applied Mathematics and Computation, Elsevier, vol. 334(C), pages 30-40.
  • Handle: RePEc:eee:apmaco:v:334:y:2018:i:c:p:30-40
    DOI: 10.1016/j.amc.2018.03.097
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    References listed on IDEAS

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    1. Laskin, Nick, 2017. "Time fractional quantum mechanics," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 16-28.
    2. Han, Jiangfeng & Migórski, Stanisław & Zeng, Huidan, 2017. "Weak solvability of a fractional viscoelastic frictionless contact problem," Applied Mathematics and Computation, Elsevier, vol. 303(C), pages 1-18.
    3. Sun, HongGuang & Li, Zhipeng & Zhang, Yong & Chen, Wen, 2017. "Fractional and fractal derivative models for transient anomalous diffusion: Model comparison," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 346-353.
    4. Zhou, Fengying & Xu, Xiaoyong, 2016. "The third kind Chebyshev wavelets collocation method for solving the time-fractional convection diffusion equations with variable coefficients," Applied Mathematics and Computation, Elsevier, vol. 280(C), pages 11-29.
    5. Zhang, Yong & Sun, HongGuang & Stowell, Harold H. & Zayernouri, Mohsen & Hansen, Samantha E., 2017. "A review of applications of fractional calculus in Earth system dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 29-46.
    6. Prakash, Amit & Kumar, Manoj & Sharma, Kapil K., 2015. "Numerical method for solving fractional coupled Burgers equations," Applied Mathematics and Computation, Elsevier, vol. 260(C), pages 314-320.
    7. Singh, Harendra, 2018. "Approximate solution of fractional vibration equation using Jacobi polynomials," Applied Mathematics and Computation, Elsevier, vol. 317(C), pages 85-100.
    8. Prakash, Amit & Kaur, Hardish, 2017. "Numerical solution for fractional model of Fokker-Planck equation by using q-HATM," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 99-110.
    9. Singh, Jagdev & Kumar, Devendra & Hammouch, Zakia & Atangana, Abdon, 2018. "A fractional epidemiological model for computer viruses pertaining to a new fractional derivative," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 504-515.
    10. Wang, Ying & Liu, Lishan & Zhang, Xinguang & Wu, Yonghong, 2015. "Positive solutions of an abstract fractional semipositone differential system model for bioprocesses of HIV infection," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 312-324.
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