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Abundant analytical and numerical solutions of the fractional microbiological densities model in bacteria cell as a result of diffusion mechanisms

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  • Khater, Mostafa M.A.
  • Attia, Raghda A.M.
  • Abdel-Aty, Abdel-Haleem
  • Alharbi, W.
  • Lu, Dianchen

Abstract

In this paper, an analytical scheme [the generalized Sinh–Gordon equation method) with a new fractional operator (ABR fractional operator] is employed to find novel computational solutions of the nonlinear fractional Kolmogorov–Petrovskii–Piskunov (FKPP) equation. These solutions are used to evaluate the initial and boundary conditions under the numerical scheme (B-spline schemes) to get the numerical solutions of the same model. This equation describes the behavior of genetic models in the increase of microorganisms. Usually, it is used as a biological model to investigate the microbiological densities in bacteria cells as a result of diffusion mechanisms in terms of space–time. Some novel computational solutions are obtained, and the accuracy of them is investigated by calculating the absolute value of error between the obtained computational and numerical solutions. The comparison between the distinct types of obtained solutions is shown by calculating the absolute value of error.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:136:y:2020:i:c:s0960077920302241
    DOI: 10.1016/j.chaos.2020.109824
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    References listed on IDEAS

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    1. Fernandez, Arran & Özarslan, Mehmet Ali & Baleanu, Dumitru, 2019. "On fractional calculus with general analytic kernels," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 248-265.
    2. Owolabi, Kolade M. & Hammouch, Zakia, 2019. "Spatiotemporal patterns in the Belousov–Zhabotinskii reaction systems with Atangana–Baleanu fractional order derivative," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1072-1090.
    3. Hajipour, Mojtaba & Jajarmi, Amin & Malek, Alaeddin & Baleanu, Dumitru, 2018. "Positivity-preserving sixth-order implicit finite difference weighted essentially non-oscillatory scheme for the nonlinear heat equation," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 146-158.
    4. Ghanbari, Behzad & Kumar, Sunil & Kumar, Ranbir, 2020. "A study of behaviour for immune and tumor cells in immunogenetic tumour model with non-singular fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
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    Cited by:

    1. Mostafa M. A. Khater & Aliaa Mahfooz Alabdali, 2021. "Multiple Novels and Accurate Traveling Wave and Numerical Solutions of the (2+1) Dimensional Fisher-Kolmogorov- Petrovskii-Piskunov Equation," Mathematics, MDPI, vol. 9(12), pages 1-13, June.
    2. Abdullah, & Ahmad, Saeed & Owyed, Saud & Abdel-Aty, Abdel-Haleem & Mahmoud, Emad E. & Shah, Kamal & Alrabaiah, Hussam, 2021. "Mathematical analysis of COVID-19 via new mathematical model," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).

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