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On semi analytical and numerical simulations for a mathematical biological model; the time-fractional nonlinear Kolmogorov–Petrovskii–Piskunov (KPP) equation

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  • Khater, Mostafa M.A.
  • Mohamed, Mohamed S.
  • Attia, Raghda A.M.

Abstract

Through five latest numerical schemes (Adomian decomposition (AD), El Kalla (EK), cubic B - spline (CBS), expanded Cubic B-Spline (ECBS), exponential cubic B - spline (ExCBS), this manuscript examines semi-analytical and numerical solutions of the time-fractional nonlinear Kolmogorov–Petrovskii–Piskunov (KPP) equation. Using the Caputo–Fabrizio fractional derivative and expanded Riccati - expansion process in Hamed et al.(2020) [1], developed computational solutions are investigated to determine the sufficient conditions for the implementation of the above-suggested schemes. In combustion theory, mathematical biology, and other study fields, the quasi-linear model is parabolic in simulating specific reaction-diffusion systems. The model’s solution represents the proliferation of a favored gene, and moving waves are pursued by nonlinear interaction. By measuring the absolute error between the exact and numerical solutions, the obtained numerical solutions’ consistency is examined. To explain the correspondence between the exact and numerical solutions, several sketches are given.

Suggested Citation

  • Khater, Mostafa M.A. & Mohamed, Mohamed S. & Attia, Raghda A.M., 2021. "On semi analytical and numerical simulations for a mathematical biological model; the time-fractional nonlinear Kolmogorov–Petrovskii–Piskunov (KPP) equation," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    • Handle: RePEc:eee:chsofr:v:144:y:2021:i:c:s0960077921000291
    DOI: 10.1016/j.chaos.2021.110676
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    References listed on IDEAS

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    1. Rahmat Ellahi & Constantin Fetecau & Mohsen Sheikholeslami, 2018. "Recent Advances in the Application of Differential Equations in Mechanical Engineering Problems," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-3, March.
    2. Khader, M.M. & Saad, K.M., 2018. "A numerical approach for solving the fractional Fisher equation using Chebyshev spectral collocation method," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 169-177.
    3. Zhang, P. & Xiao, X. & Ma, Z.W., 2016. "A review of the composite phase change materials: Fabrication, characterization, mathematical modeling and application to performance enhancement," Applied Energy, Elsevier, vol. 165(C), pages 472-510.
    4. Ali, Ahmad T. & Khater, Mostafa M.A. & Attia, Raghda A.M. & Abdel-Aty, Abdel-Haleem & Lu, Dianchen, 2020. "Abundant numerical and analytical solutions of the generalized formula of Hirota-Satsuma coupled KdV system," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
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    Cited by:

    1. Khater, Mostafa M.A., 2023. "Multi-vector with nonlocal and non-singular kernel ultrashort optical solitons pulses waves in birefringent fibers," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    2. Khater, Mostafa M.A., 2022. "De Broglie waves and nuclear element interaction; Abundant waves structures of the nonlinear fractional Phi-four equation," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    3. Khater, Mostafa M.A., 2023. "A hybrid analytical and numerical analysis of ultra-short pulse phase shifts," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).

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