IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v178y2024ics0960077923012493.html
   My bibliography  Save this article

Efficient solutions for fractional Tsunami shallow-water mathematical model: A comparative study via semi analytical techniques

Author

Listed:
  • Ali, Khalid K.
  • Wazwaz, Abdul-Majid
  • Maneea, M.

Abstract

In this study, we delve into the effective solution of the fractional tsunami shallow-water mathematical model. Tsunami propagation and inundation modeling is of paramount importance for hazard assessment and disaster preparedness. By employing two distinct semi-analytical techniques: the residual power series method and the modified Taylor series method, we obtain approximate solutions for the tsunami mathematical model. Solutions for varying coastal inclinations and ocean depths have been acquired for the given model taking into consideration the changes in coastal gradient and ocean depth and how to impact tsunami wave velocity and wave amplification at different values of the fractional order derivative and different steps of time. The utilized semi analytical techniques generate the solution in the form of power series expansion, so the convergence study is implemented. In order to prove the efficiency of the proposed methods, several tables for comparisons between our results and other numerical results from literature are presented. Also graphs of the obtained solutions introduced in two and three dimensions.

Suggested Citation

  • Ali, Khalid K. & Wazwaz, Abdul-Majid & Maneea, M., 2024. "Efficient solutions for fractional Tsunami shallow-water mathematical model: A comparative study via semi analytical techniques," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    • Handle: RePEc:eee:chsofr:v:178:y:2024:i:c:s0960077923012493
    DOI: 10.1016/j.chaos.2023.114347
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077923012493
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2023.114347?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Veeresha, P., 2022. "The efficient fractional order based approach to analyze chemical reaction associated with pattern formation," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    2. Bochao Chen & Li Qin & Fei Xu & Jian Zu, 2018. "Applications of General Residual Power Series Method to Differential Equations with Variable Coefficients," Discrete Dynamics in Nature and Society, Hindawi, vol. 2018, pages 1-9, July.
    3. Ilhan, Esin & Veeresha, P. & Baskonus, Haci Mehmet, 2021. "Fractional approach for a mathematical model of atmospheric dynamics of CO2 gas with an efficient method," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    4. Deepika, S. & Veeresha, P., 2023. "Dynamics of chaotic waterwheel model with the asymmetric flow within the frame of Caputo fractional operator," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    5. El-Ajou, Ahmad & Abu Arqub, Omar & Al-Smadi, Mohammed, 2015. "A general form of the generalized Taylor’s formula with some applications," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 851-859.
    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. Alquran, Marwan & Yousef, Feras & Alquran, Farah & Sulaiman, Tukur A. & Yusuf, Abdullahi, 2021. "Dual-wave solutions for the quadratic–cubic conformable-Caputo time-fractional Klein–Fock–Gordon equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 62-76.
    2. Asjad, Muhammad Imran & Sunthrayuth, Pongsakorn & Ikram, Muhammad Danish & Muhammad, Taseer & Alshomrani, Ali Saleh, 2022. "Analysis of non-singular fractional bioconvection and thermal memory with generalized Mittag-Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    3. Arqub, Omar Abu & Maayah, Banan, 2019. "Fitted fractional reproducing kernel algorithm for the numerical solutions of ABC – Fractional Volterra integro-differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 394-402.
    4. Rashid, Saima & Jarad, Fahd & Alsharidi, Abdulaziz Khalid, 2022. "Numerical investigation of fractional-order cholera epidemic model with transmission dynamics via fractal–fractional operator technique," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    5. Zulqurnain Sabir & Thongchai Botmart & Muhammad Asif Zahoor Raja & Wajaree Weera, 2022. "An advanced computing scheme for the numerical investigations of an infection-based fractional-order nonlinear prey-predator system," PLOS ONE, Public Library of Science, vol. 17(3), pages 1-13, March.
    6. Jaradat, I. & Al-Dolat, M. & Al-Zoubi, K. & Alquran, M., 2018. "Theory and applications of a more general form for fractional power series expansion," Chaos, Solitons & Fractals, Elsevier, vol. 108(C), pages 107-110.
    7. Shadimetov, Kh.M. & Hayotov, A.R. & Nuraliev, F.A., 2016. "Optimal quadrature formulas of Euler–Maclaurin type," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 340-355.
    8. Mohammed Shqair & Ahmad El-Ajou & Mazen Nairat, 2019. "Analytical Solution for Multi-Energy Groups of Neutron Diffusion Equations by a Residual Power Series Method," Mathematics, MDPI, vol. 7(7), pages 1-20, July.
    9. Karimov, Artur & Kopets, Ekaterina & Karimov, Timur & Almjasheva, Oksana & Arlyapov, Viacheslav & Butusov, Denis, 2023. "Empirically developed model of the stirring-controlled Belousov–Zhabotinsky reaction," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    10. Aylin Bayrak, Mine & Demir, Ali, 2018. "A new approach for space-time fractional partial differential equations by residual power series method," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 215-230.
    11. Guirao, Juan Luis García & Alsulami, Mansoor & Baskonus, Haci Mehmet & Ilhan, Esin & Veeresha, P., 2023. "Analysis of nonlinear compartmental model using a reliable method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 214(C), pages 133-151.
    12. Stefania Tomasiello & Jorge E. Macías-Díaz, 2023. "A Mini-Review on Recent Fractional Models for Agri-Food Problems," Mathematics, MDPI, vol. 11(10), pages 1-12, May.

    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:eee:chsofr:v:178:y:2024:i:c:s0960077923012493. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.