IDEAS home Printed from https://ideas.repec.org/a/wly/jnlaaa/v2012y2012i1n752869.html

Approximate Solutions of Fractional Nonlinear Equations Using Homotopy Perturbation Transformation Method

Author

Listed:
  • Yanqin Liu

Abstract

A homotopy perturbation transformation method (HPTM) which is based on homotopy perturbation method and Laplace transform is first applied to solve the approximate solution of the fractional nonlinear equations. The nonlinear terms can be easily handled by the use of He′s polynomials. Illustrative examples are included to demonstrate the high accuracy and fast convergence of this new algorithm.

Suggested Citation

  • Yanqin Liu, 2012. "Approximate Solutions of Fractional Nonlinear Equations Using Homotopy Perturbation Transformation Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:752869
    DOI: 10.1155/2012/752869
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2012/752869
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2012/752869?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
    ---><---

    References listed on IDEAS

    as
    1. Ghorbani, Asghar, 2009. "Beyond Adomian polynomials: He polynomials," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1486-1492.
    2. He, Ji-Huan, 2005. "Application of homotopy perturbation method to nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 695-700.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yanqin Liu & Fengsheng Xu & Xiuling Yin, 2013. "Variational Approximate Solutions of Fractional Nonlinear Nonhomogeneous Equations with Laplace Transform," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Limei Yan, 2013. "Numerical Solutions of Fractional Fokker‐Planck Equations Using Iterative Laplace Transform Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. Saha Ray, S. & Sahoo, S., 2015. "A comparative study on the analytic solutions of fractional coupled sine–Gordon equations by using two reliable methods," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 72-82.
    4. M. A. Mohamed & M. Sh. Torky, 2014. "Approximate Solution of Fractional Nonlinear Partial Differential Equations by the Legendre Multiwavelet Galerkin Method," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    5. Yanqin Liu & Limei Yan, 2013. "Solutions of Fractional Konopelchenko‐Dubrovsky and Nizhnik‐Novikov‐Veselov Equations Using a Generalized Fractional Subequation Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    6. Benito Chen-Charpentier & Gilberto González-Parra & Abraham J. Arenas, 2016. "Fractional Order Financial Models for Awareness and Trial Advertising Decisions," Computational Economics, Springer;Society for Computational Economics, vol. 48(4), pages 555-568, December.
    7. Hegagi Mohamed Ali & Ismail Gad Ameen, 2019. "An Efficient Approach for Solving Fractional Dynamics of a Predator-Prey System," Modern Applied Science, Canadian Center of Science and Education, vol. 13(11), pages 116-116, November.
    8. Arenas, Abraham J. & González-Parra, Gilberto & Chen-Charpentier, Benito M., 2016. "Construction of nonstandard finite difference schemes for the SI and SIR epidemic models of fractional order," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 121(C), pages 48-63.

    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. Shidfar, A. & Molabahrami, A. & Babaei, A. & Yazdanian, A., 2009. "A study on the d-dimensional Schrödinger equation with a power-law nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2154-2158.
    2. Hegagi Mohamed Ali & Ismail Gad Ameen, 2019. "An Efficient Approach for Solving Fractional Dynamics of a Predator-Prey System," Modern Applied Science, Canadian Center of Science and Education, vol. 13(11), pages 116-116, November.
    3. Hradyesh Kumar Mishra & Atulya K. Nagar, 2012. "He‐Laplace Method for Linear and Nonlinear Partial Differential Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    4. Abdolamir Karbalaie & Hamed Hamid Muhammed & Bjorn-Erik Erlandsson, 2013. "Using Homo-Separation of Variables for Solving Systems of Nonlinear Fractional Partial Differential Equations," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2013, pages 1-8, June.
    5. Ji-Huan He, 2012. "Asymptotic Methods for Solitary Solutions and Compactons," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    6. S. S. Nourazar & M. Habibi Matin & M. Simiari, 2011. "The HPM Applied to MHD Nanofluid Flow over a Horizontal Stretching Plate," Journal of Applied Mathematics, John Wiley & Sons, vol. 2011(1).
    7. Shweta, & Arora, Gourav & Kumar, Rajesh, 2025. "Large time solution for collisional breakage model: Laplace transformation based accelerated homotopy perturbation method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 230(C), pages 39-52.
    8. He, Ji-Huan, 2009. "Nonlinear science as a fluctuating research frontier," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2533-2537.
    9. Abbasbandy, S., 2007. "A numerical solution of Blasius equation by Adomian’s decomposition method and comparison with homotopy perturbation method," Chaos, Solitons & Fractals, Elsevier, vol. 31(1), pages 257-260.
    10. Çelik, Nisa & Seadawy, Aly R. & Sağlam Özkan, Yeşim & Yaşar, Emrullah, 2021. "A model of solitary waves in a nonlinear elastic circular rod: Abundant different type exact solutions and conservation laws," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    11. Javidi, M. & Golbabai, A., 2008. "Exact and numerical solitary wave solutions of generalized Zakharov equation by the variational iteration method," Chaos, Solitons & Fractals, Elsevier, vol. 36(2), pages 309-313.
    12. Amit K Verma & Biswajit Pandit & Ravi P. Agarwal, 2021. "Analysis and Computation of Solutions for a Class of Nonlinear SBVPs Arising in Epitaxial Growth," Mathematics, MDPI, vol. 9(7), pages 1-25, April.
    13. Alipanah, Amjad & Zafari, Mahnaz, 2023. "Collocation method using auto-correlation functions of compact supported wavelets for solving Volterra’s population model," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    14. Ya Qin & Adnan Khan & Izaz Ali & Maysaa Al Qurashi & Hassan Khan & Rasool Shah & Dumitru Baleanu, 2020. "An Efficient Analytical Approach for the Solution of Certain Fractional-Order Dynamical Systems," Energies, MDPI, vol. 13(11), pages 1-14, May.
    15. Mohamed. Z. Mohamed & Mohammed Yousif & Amjad E. Hamza, 2022. "Solving Nonlinear Fractional Partial Differential Equations Using the Elzaki Transform Method and the Homotopy Perturbation Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2022(1).
    16. Lv, Jian Cheng & Yi, Zhang, 2007. "Some chaotic behaviors in a MCA learning algorithm with a constant learning rate," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 1040-1047.
    17. Xu, Lan, 2008. "Variational approach to solitons of nonlinear dispersive K(m,n) equations," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 137-143.
    18. Emad H. Aly & Abdelhalim Ebaid, 2013. "New Analytical and Numerical Solutions for Mixed Convection Boundary‐Layer Nanofluid Flow along an Inclined Plate Embedded in a Porous Medium," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    19. M. S. H. Chowdhury & I. Hashim & S. Momani & M. M. Rahman, 2012. "Application of Multistage Homotopy Perturbation Method to the Chaotic Genesio System," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    20. Yu, Guo-Fu & Tam, Hon-Wah, 2006. "Conservation laws for two (2+1)-dimensional differential–difference systems," Chaos, Solitons & Fractals, Elsevier, vol. 30(1), pages 189-196.

    More about this item

    Statistics

    Access and download statistics

    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:wly:jnlaaa:v:2012:y:2012:i:1:n:752869. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4058 .

    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.