IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i2p155-d479497.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/2/155/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/2/155/
    Download Restriction: no
    ---><---

    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. 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.
    4. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Prakash, Amit & Kaur, Hardish, 2021. "Analysis and numerical simulation of fractional Biswas–Milovic model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 298-315.
    2. Sunil Kumar & Ali Ahmadian & Ranbir Kumar & Devendra Kumar & Jagdev Singh & Dumitru Baleanu & Mehdi Salimi, 2020. "An Efficient Numerical Method for Fractional SIR Epidemic Model of Infectious Disease by Using Bernstein Wavelets," Mathematics, MDPI, vol. 8(4), pages 1-22, April.
    3. Cao, Yan & Zhou, Wei-Jie & Liu, Xiao-Zhen & Wu, Kai-Ning, 2024. "Passivity of fractional reaction-diffusion systems," Applied Mathematics and Computation, Elsevier, vol. 476(C).
    4. Samad Noeiaghdam & Aliona Dreglea & Hüseyin Işık & Muhammad Suleman, 2021. "A Comparative Study between Discrete Stochastic Arithmetic and Floating-Point Arithmetic to Validate the Results of Fractional Order Model of Malaria Infection," Mathematics, MDPI, vol. 9(12), pages 1-17, June.
    5. Samad Noeiaghdam & Sanda Micula & Juan J. Nieto, 2021. "A Novel Technique to Control the Accuracy of a Nonlinear Fractional Order Model of COVID-19: Application of the CESTAC Method and the CADNA Library," Mathematics, MDPI, vol. 9(12), pages 1-26, June.
    6. Jing Chang & Jin Zhang & Ming Cai, 2021. "Series Solutions of High-Dimensional Fractional Differential Equations," Mathematics, MDPI, vol. 9(17), pages 1-21, August.
    7. Gómez-Aguilar, J.F., 2020. "Chaos and multiple attractors in a fractal–fractional Shinriki’s oscillator model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 539(C).
    8. Ndaïrou, Faïçal & Area, Iván & Nieto, Juan J. & Silva, Cristiana J. & Torres, Delfim F.M., 2021. "Fractional model of COVID-19 applied to Galicia, Spain and Portugal," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    9. Sadat, R. & Saleh, R. & Kassem, M. & Mousa, Mohamed M., 2020. "Investigation of Lie symmetry and new solutions for highly dimensional non-elastic and elastic interactions between internal waves," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    10. Bhatter, Sanjay & Mathur, Amit & Kumar, Devendra & Nisar, Kottakkaran Sooppy & Singh, Jagdev, 2020. "Fractional modified Kawahara equation with Mittag–Leffler law," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    11. Bansal, Komal & Mathur, Trilok & Agarwal, Shivi, 2023. "Fractional-order crime propagation model with non-linear transmission rate," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    12. Abidemi, Afeez & Owolabi, Kolade M. & Pindza, Edson, 2022. "Modelling the transmission dynamics of Lassa fever with nonlinear incidence rate and vertical transmission," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 597(C).
    13. Mohamed Kharrat & Hassen Arfaoui, 2023. "A New Stabled Relaxation Method for Pricing European Options Under the Time-Fractional Vasicek Model," Computational Economics, Springer;Society for Computational Economics, vol. 61(4), pages 1745-1763, April.
    14. Rayal, Ashish & Ram Verma, Sag, 2020. "Numerical analysis of pantograph differential equation of the stretched type associated with fractal-fractional derivatives via fractional order Legendre wavelets," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    15. Joshi, Divya D. & Bhalekar, Sachin & Gade, Prashant M., 2023. "Controlling fractional difference equations using feedback," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    16. Saad, Khaled M. & Gómez-Aguilar, J.F. & Almadiy, Abdulrhman A., 2020. "A fractional numerical study on a chronic hepatitis C virus infection model with immune response," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    17. Bhatter, Sanjay & Mathur, Amit & Kumar, Devendra & Singh, Jagdev, 2020. "A new analysis of fractional Drinfeld–Sokolov–Wilson model with exponential memory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    18. Mohamed Kharrat, 2023. "Stability Analysis for Pricing European Options Regarding the Interest Rate Generated by the Time Fractional Cox-Ingersoll-Ross Processes," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-13, June.
    19. Dwivedi, Kushal Dhar & Singh, Jagdev, 2021. "Numerical solution of two-dimensional fractional-order reaction advection sub-diffusion equation with finite-difference Fibonacci collocation method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 38-50.
    20. Attaullah, & Jan, Rashid & Yüzbaşı, Şuayip, 2021. "Dynamical behaviour of HIV Infection with the influence of variable source term through Galerkin method," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2021:i:2:p:155-:d:479497. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.