IDEAS home Printed from https://ideas.repec.org/a/wly/jnlaaa/v2013y2013i1n351057.html

Local Fractional Series Expansion Method for Solving Wave and Diffusion Equations on Cantor Sets

Author

Listed:
  • Ai-Min Yang
  • Xiao-Jun Yang
  • Zheng-Biao Li

Abstract

We proposed a local fractional series expansion method to solve the wave and diffusion equations on Cantor sets. Some examples are given to illustrate the efficiency and accuracy of the proposed method to obtain analytical solutions to differential equations within the local fractional derivatives.

Suggested Citation

  • Ai-Min Yang & Xiao-Jun Yang & Zheng-Biao Li, 2013. "Local Fractional Series Expansion Method for Solving Wave and Diffusion Equations on Cantor Sets," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:351057
    DOI: 10.1155/2013/351057
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2013/351057
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2013/351057?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. Jumarie, Guy, 2009. "Probability calculus of fractional order and fractional Taylor’s series application to Fokker–Planck equation and information of non-random functions," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1428-1448.
    2. Ming-Sheng Hu & Ravi P. Agarwal & Xiao-Jun Yang, 2012. "Local Fractional Fourier Series with Application to Wave Equation in Fractal Vibrating String," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-15, December.
    3. Ming-Sheng Hu & Ravi P. Agarwal & Xiao-Jun Yang, 2012. "Local Fractional Fourier Series with Application to Wave Equation in Fractal Vibrating String," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    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. Hassan Kamil Jassim, 2016. "The Approximate Solutions of Three‐Dimensional Diffusion and Wave Equations within Local Fractional Derivative Operator," Abstract and Applied Analysis, John Wiley & Sons, vol. 2016(1).
    2. Ai-Min Yang & Yu-Zhu Zhang & Carlo Cattani & Gong-Nan Xie & Mohammad Mehdi Rashidi & Yi-Jun Zhou & Xiao-Jun Yang, 2014. "Application of Local Fractional Series Expansion Method to Solve Klein‐Gordon Equations on Cantor Sets," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    3. Yang Zhao & De-Fu Cheng & Xiao-Jun Yang, 2013. "Approximation Solutions for Local Fractional Schrödinger Equation in the One‐Dimensional Cantorian System," Advances in Mathematical Physics, John Wiley & Sons, vol. 2013(1).
    4. Xiao-Jun Yang & Dumitru Baleanu & H. M. Srivastava & J. A. Tenreiro Machado, 2013. "On Local Fractional Continuous Wavelet Transform," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    5. Ai-Min Yang & Zeng-Shun Chen & H. M. Srivastava & Xiao-Jun Yang, 2013. "Application of the Local Fractional Series Expansion Method and the Variational Iteration Method to the Helmholtz Equation Involving Local Fractional Derivative Operators," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    6. Guang-Sheng Chen & H. M. Srivastava & Pin Wang & Wei Wei, 2014. "Some Further Generalizations of Hölder′s Inequality and Related Results on Fractal Space," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    7. Sheng-Ping Yan & Hossein Jafari & Hassan Kamil Jassim, 2014. "Local Fractional Adomian Decomposition and Function Decomposition Methods for Laplace Equation within Local Fractional Operators," Advances in Mathematical Physics, John Wiley & Sons, vol. 2014(1).
    8. Dumitru Baleanu & J. A. Tenreiro Machado & Carlo Cattani & Mihaela Cristina Baleanu & Xiao-Jun Yang, 2014. "Local Fractional Variational Iteration and Decomposition Methods for Wave Equation on Cantor Sets within Local Fractional Operators," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

    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. Yong-Ju Yang & Dumitru Baleanu & Xiao-Jun Yang, 2013. "Analysis of Fractal Wave Equations by Local Fractional Fourier Series Method," Advances in Mathematical Physics, John Wiley & Sons, vol. 2013(1).
    2. Yang Zhao & Dumitru Baleanu & Mihaela Cristina Baleanu & De-Fu Cheng & Xiao-Jun Yang, 2013. "Mappings for Special Functions on Cantor Sets and Special Integral Transforms via Local Fractional Operators," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. Yong-Ju Yang & Dumitru Baleanu & Xiao-Jun Yang, 2013. "A Local Fractional Variational Iteration Method for Laplace Equation within Local Fractional Operators," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    4. Yu Zhang, 2014. "Solving Initial‐Boundary Value Problems for Local Fractional Differential Equation by Local Fractional Fourier Series Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    5. Zhi-Yong Chen & Carlo Cattani & Wei-Ping Zhong, 2014. "Signal Processing for Nondifferentiable Data Defined on Cantor Sets: A Local Fractional Fourier Series Approach," Advances in Mathematical Physics, John Wiley & Sons, vol. 2014(1).
    6. Yong-Ju Yang & Liu-Qing Hua, 2014. "Variational Iteration Transform Method for Fractional Differential Equations with Local Fractional Derivative," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    7. Ya-Juan Hao & H. M. Srivastava & Hossein Jafari & Xiao-Jun Yang, 2013. "Helmholtz and Diffusion Equations Associated with Local Fractional Derivative Operators Involving the Cantorian and Cantor‐Type Cylindrical Coordinates," Advances in Mathematical Physics, John Wiley & Sons, vol. 2013(1).
    8. Guang-Sheng Chen & H. M. Srivastava & Pin Wang & Wei Wei, 2014. "Some Further Generalizations of Hölder′s Inequality and Related Results on Fractal Space," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    9. Sheng-Ping Yan & Hossein Jafari & Hassan Kamil Jassim, 2014. "Local Fractional Adomian Decomposition and Function Decomposition Methods for Laplace Equation within Local Fractional Operators," Advances in Mathematical Physics, John Wiley & Sons, vol. 2014(1).
    10. Nabard Habibi & Zohre Nouri, 2020. "Application of Local Fractional Homotopy Perturbation Method in Physical Problems," Advances in Mathematical Physics, John Wiley & Sons, vol. 2020(1).
    11. Shun-Qin Wang & Yong-Ju Yang & Hassan Kamil Jassim, 2014. "Local Fractional Function Decomposition Method for Solving Inhomogeneous Wave Equations with Local Fractional Derivative," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    12. Yang Zhao & De-Fu Cheng & Xiao-Jun Yang, 2013. "Approximation Solutions for Local Fractional Schrödinger Equation in the One‐Dimensional Cantorian System," Advances in Mathematical Physics, John Wiley & Sons, vol. 2013(1).
    13. Ming-Sheng Hu & Ravi P. Agarwal & Xiao-Jun Yang, 2012. "Local Fractional Fourier Series with Application to Wave Equation in Fractal Vibrating String," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    14. Jumarie, Guy, 2009. "From Lagrangian mechanics fractal in space to space fractal Schrödinger’s equation via fractional Taylor’s series," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1590-1604.

    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:2013:y:2013:i:1:n:351057. 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.