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On the Analytical and Numerical Solutions in the Quantum Magnetoplasmas: The Atangana Conformable Derivative (1 + 3)‐ZK Equation with Power‐Law Nonlinearity

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  • Mostafa M. A. Khater
  • Yu-Ming Chu
  • Raghda A. M. Attia
  • Mustafa Inc
  • Dianchen Lu

Abstract

In this research paper, our work is connected with one of the most popular models in quantum magnetoplasma applications. The computational wave and numerical solutions of the Atangana conformable derivative (1 + 3)‐Zakharov‐Kuznetsov (ZK) equation with power‐law nonlinearity are investigated via the modified Khater method and septic‐B‐spline scheme. This model is formulated and derived by employing the well‐known reductive perturbation method. Applying the modified Khater (mK) method, septic B‐spline scheme to the (1 + 3)‐ZK equation with power‐law nonlinearity after harnessing suitable wave transformation gives plentiful unprecedented ion‐solitary wave solutions. Stability property is checked for our results to show their applicability for applying in the model’s applications. The result solutions are constructed along with their 2D, 3D, and contour graphical configurations for clarity and exactitude.

Suggested Citation

  • Mostafa M. A. Khater & Yu-Ming Chu & Raghda A. M. Attia & Mustafa Inc & Dianchen Lu, 2020. "On the Analytical and Numerical Solutions in the Quantum Magnetoplasmas: The Atangana Conformable Derivative (1 + 3)‐ZK Equation with Power‐Law Nonlinearity," Advances in Mathematical Physics, John Wiley & Sons, vol. 2020(1).
    • Handle: RePEc:wly:jnlamp:v:2020:y:2020:i:1:n:5809289
    DOI: 10.1155/2020/5809289
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    References listed on IDEAS

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    1. Korpinar, Zeliha & Inc, Mustafa & Bayram, Mustafa, 2020. "Theory and application for the system of fractional Burger equations with Mittag leffler kernel," Applied Mathematics and Computation, Elsevier, vol. 367(C).
    2. Ávalos-Ruiz, L.F. & Gómez-Aguilar, J.F. & Atangana, A. & Owolabi, Kolade M., 2019. "On the dynamics of fractional maps with power-law, exponential decay and Mittag–Leffler memory," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 364-388.
    3. Khater, Mostafa M.A. & Attia, Raghda A.M. & Abdel-Aty, Abdel-Haleem & Alharbi, W. & Lu, Dianchen, 2020. "Abundant analytical and numerical solutions of the fractional microbiological densities model in bacteria cell as a result of diffusion mechanisms," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    4. Abdel-Haleem Abdel-Aty & Mostafa M. A. Khater & Raghda A. M. Attia & Hichem Eleuch, 2020. "Exact Traveling and Nano-Solitons Wave Solitons of the Ionic Waves Propagating along Microtubules in Living Cells," Mathematics, MDPI, vol. 8(5), pages 1-11, May.
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