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Aboodh Transform Iterative Method for Spatial Diffusion of a Biological Population with Fractional-Order

Author

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  • Gbenga O. Ojo

    (Department of Mathematics, Eastern Mediterranean University, Via Mersir-10, TR 99628 Famagusta, Turkey)

  • Nazim I. Mahmudov

    (Department of Mathematics, Eastern Mediterranean University, Via Mersir-10, TR 99628 Famagusta, Turkey)

Abstract

In this paper, a new approximate analytical method is proposed for solving the fractional biological population model, the fractional derivative is described in the Caputo sense. This method is based upon the Aboodh transform method and the new iterative method, the Aboodh transform is a modification of the Laplace transform. Illustrative cases are considered and the comparison between exact solutions and numerical solutions are considered for different values of alpha. Furthermore, the surface plots are provided in order to understand the effect of the fractional order. The advantage of this method is that it is efficient, precise, and easy to implement with less computational effort.

Suggested Citation

  • Gbenga O. Ojo & Nazim I. Mahmudov, 2021. "Aboodh Transform Iterative Method for Spatial Diffusion of a Biological Population with Fractional-Order," Mathematics, MDPI, vol. 9(2), pages 1-21, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:2:p:155-:d:479497
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    References listed on IDEAS

    as
    1. Wenjin Li & Yanni Pang, 2018. "An Iterative Method for Time-Fractional Swift-Hohenberg Equation," Advances in Mathematical Physics, Hindawi, vol. 2018, pages 1-13, September.
    2. Naik, Parvaiz Ahmad & Zu, Jian & Owolabi, Kolade M., 2020. "Global dynamics of a fractional order model for the transmission of HIV epidemic with optimal control," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    3. Fei Xu & Yixian Gao & Weipeng Zhang, 2015. "Construction of Analytic Solution for Time-Fractional Boussinesq Equation Using Iterative Method," Advances in Mathematical Physics, Hindawi, vol. 2015, pages 1-7, November.
    4. Hassan Khan & Adnan Khan & Maysaa Al Qurashi & Dumitru Baleanu & Rasool Shah, 2020. "An Analytical Investigation of Fractional-Order Biological Model Using an Innovative Technique," Complexity, Hindawi, vol. 2020, pages 1-13, April.
    5. Goswami, Amit & Singh, Jagdev & Kumar, Devendra & Sushila,, 2019. "An efficient analytical approach for fractional equal width equations describing hydro-magnetic waves in cold plasma," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 563-575.
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