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Local Fractional Function Decomposition Method for Solving Inhomogeneous Wave Equations with Local Fractional Derivative

Author

Listed:
  • Shun-Qin Wang
  • Yong-Ju Yang
  • Hassan Kamil Jassim

Abstract

We propose the local fractional function decomposition method, which is derived from the coupling method of local fractional Fourier series and Yang‐Laplace transform. The forms of solutions for local fractional differential equations are established. Some examples for inhomogeneous wave equations are given to show the accuracy and efficiency of the presented technique.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:176395
    DOI: 10.1155/2014/176395
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    References listed on IDEAS

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    1. Hadi Karami & Azizollah Babakhani & Dumitru Baleanu, 2013. "Existence Results for a Class of Fractional Differential Equations with Periodic Boundary Value Conditions and with Delay," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, September.
    2. Hadi Karami & Azizollah Babakhani & Dumitru Baleanu, 2013. "Existence Results for a Class of Fractional Differential Equations with Periodic Boundary Value Conditions and with Delay," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. Abdon Atangana & Adem Kılıçman, 2013. "Analytical Solutions of Boundary Values Problem of 2D and 3D Poisson and Biharmonic Equations by Homotopy Decomposition Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
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    5. Jie Fan & Jihuan He, 2012. "Fractal Derivative Model for Air Permeability in Hierarchic Porous Media," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-7, November.
    6. 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.
    7. Jie Fan & Jihuan He, 2012. "Fractal Derivative Model for Air Permeability in Hierarchic Porous Media," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    8. Abdon Atangana & Adem Kılıçman, 2013. "Analytical Solutions of Boundary Values Problem of 2D and 3D Poisson and Biharmonic Equations by Homotopy Decomposition Method," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, September.
    9. H. Jafari & H. Tajadodi, 2010. "He's Variational Iteration Method for Solving Fractional Riccati Differential Equation," International Journal of Differential Equations, Hindawi, vol. 2010, pages 1-8, March.
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    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. Yuan Cao & Wei-Gang Ma & Lian-Chuan Ma, 2014. "Local Fractional Functional Method for Solving Diffusion Equations on Cantor Sets," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    4. Xiao-Jun Yang & Jordan Hristov & H. M. Srivastava & Bashir Ahmad, 2014. "Modelling Fractal Waves on Shallow Water Surfaces via Local Fractional Korteweg‐de Vries Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    5. 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).
    6. Shao-Hong Yan & Xiao-Hong Chen & Gong-Nan Xie & Carlo Cattani & Xiao-Jun Yang, 2014. "Solving Fokker‐Planck Equations on Cantor Sets Using Local Fractional Decomposition Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    7. Kai Liu & Ren-Jie Hu & Carlo Cattani & Gong-Nan Xie & Xiao-Jun Yang & Yang Zhao, 2014. "Local Fractional Z‐Transforms with Applications to Signals on Cantor Sets," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    8. H. M. Srivastava & Alireza Khalili Golmankhaneh & Dumitru Baleanu & Xiao-Jun Yang, 2014. "Local Fractional Sumudu Transform with Application to IVPs on Cantor Sets," 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).

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