IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v6y2017i1p1-d123945.html
   My bibliography  Save this article

A Numerical Solution of Fractional Lienard’s Equation by Using the Residual Power Series Method

Author

Listed:
  • Muhammed I. Syam

    (Department of Mathematical Sciences, United Arab Emirates University, Al-Ain 15551, United Arab Emirates)

Abstract

In this paper, we investigate a numerical solution of Lienard’s equation. The residual power series (RPS) method is implemented to find an approximate solution to this problem. The proposed method is a combination of the fractional Taylor series and the residual functions. Numerical and theoretical results are presented.

Suggested Citation

  • Muhammed I. Syam, 2017. "A Numerical Solution of Fractional Lienard’s Equation by Using the Residual Power Series Method," Mathematics, MDPI, vol. 6(1), pages 1-9, December.
    • Handle: RePEc:gam:jmathe:v:6:y:2017:i:1:p:1-:d:123945
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/6/1/1/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/6/1/1/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Suheil A. Khuri, 2001. "A Laplace decomposition algorithm applied to a class of nonlinear differential equations," Journal of Applied Mathematics, Hindawi, vol. 1, pages 1-15, January.
    2. Syam, Muhammed I., 2007. "The modified Broyden-variational method for solving nonlinear elliptic differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 392-404.
    3. Alquran, Marwan & Al-Khaled, Kamel & Sardar, Tridip & Chattopadhyay, Joydev, 2015. "Revisited Fisher’s equation in a new outlook: A fractional derivative approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 438(C), pages 81-93.
    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. Zhao, Dazhi & Yu, Guozhu & Tian, Yan, 2020. "Recursive formulae for the analytic solution of the nonlinear spatial conformable fractional evolution equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    2. Bothayna S. H. Kashkari & Muhammed I. Syam, 2018. "Reproducing Kernel Method for Solving Nonlinear Fractional Fredholm Integrodifferential Equation," Complexity, Hindawi, vol. 2018, pages 1-7, December.
    3. Baleanu, Dumitru & Jajarmi, Amin & Mohammadi, Hakimeh & Rezapour, Shahram, 2020. "A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    4. Muhammed I. Syam & Azza Alsuwaidi & Asia Alneyadi & Safa Al Refai & Sondos Al Khaldi, 2018. "An Implicit Hybrid Method for Solving Fractional Bagley-Torvik Boundary Value Problem," Mathematics, MDPI, vol. 6(7), pages 1-11, June.
    5. Han, Yuxin & Huang, Xin & Gu, Wei & Zheng, Bolong, 2023. "Linearized transformed L1 finite element methods for semi-linear time-fractional parabolic problems," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    6. Shah, Kamal & Alqudah, Manar A. & Jarad, Fahd & Abdeljawad, Thabet, 2020. "Semi-analytical study of Pine Wilt Disease model with convex rate under Caputo–Febrizio fractional order derivative," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    7. Dubey, Ved Prakash & Kumar, Rajnesh & Kumar, Devendra, 2020. "A hybrid analytical scheme for the numerical computation of time fractional computer virus propagation model and its stability analysis," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    8. Atangana, Abdon, 2016. "On the new fractional derivative and application to nonlinear Fisher’s reaction–diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 948-956.
    9. Akinyemi, Lanre & Şenol, Mehmet & Iyiola, Olaniyi S., 2021. "Exact solutions of the generalized multidimensional mathematical physics models via sub-equation method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 211-233.
    10. M. M. Khashshan & Muhammed I. Syam & Ahlam Al Mokhmari, 2018. "A Reliable Method for Solving Fractional Sturm–Liouville Problems," Mathematics, MDPI, vol. 6(10), pages 1-10, September.

    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:6:y:2017:i:1:p:1-:d:123945. 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.