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Mappings for Special Functions on Cantor Sets and Special Integral Transforms via Local Fractional Operators

Author

Listed:
  • Yang Zhao
  • Dumitru Baleanu
  • Mihaela Cristina Baleanu
  • De-Fu Cheng
  • Xiao-Jun Yang

Abstract

The mappings for some special functions on Cantor sets are investigated. Meanwhile, we apply the local fractional Fourier series, Fourier transforms, and Laplace transforms to solve three local fractional differential equations, and the corresponding nondifferentiable solutions were presented.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:316978
    DOI: 10.1155/2013/316978
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    References listed on IDEAS

    as
    1. Ji-Huan He, 2012. "Asymptotic Methods for Solitary Solutions and Compactons," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    2. S. J. Sadati & D. Baleanu & A. Ranjbar & R. Ghaderi & T. Abdeljawad (Maraaba), 2010. "Mittag-Leffler Stability Theorem for Fractional Nonlinear Systems with Delay," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-7, August.
    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, Hindawi, vol. 2012, pages 1-15, December.
    4. Scalas, Enrico & Gorenflo, Rudolf & Mainardi, Francesco, 2000. "Fractional calculus and continuous-time finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 284(1), pages 376-384.
    5. Mainardi, Francesco & Raberto, Marco & Gorenflo, Rudolf & Scalas, Enrico, 2000. "Fractional calculus and continuous-time finance II: the waiting-time distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 468-481.
    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, John Wiley & Sons, vol. 2012(1).
    7. S. J. Sadati & D. Baleanu & A. Ranjbar & R. Ghaderi & T. Abdeljawad (Maraaba), 2010. "Mittag‐Leffler Stability Theorem for Fractional Nonlinear Systems with Delay," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    8. Ji-Huan He, 2012. "Asymptotic Methods for Solitary Solutions and Compactons," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-130, November.
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    Cited by:

    1. 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).
    2. 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).

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