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Local Fractional Fourier Series with Application to Wave Equation in Fractal Vibrating String

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  • Ming-Sheng Hu
  • Ravi P. Agarwal
  • Xiao-Jun Yang

Abstract

We introduce the wave equation in fractal vibrating string in the framework of the local fractional calculus. Our particular attention is devoted to the technique of the local fractional Fourier series for processing these local fractional differential operators in a way accessible to applied scientists. By applying this technique we derive the local fractional Fourier series solution of the local fractional wave equation in fractal vibrating string and show the fundamental role of the Mittag-Leffler function.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jnlaaa:567401
    DOI: 10.1155/2012/567401
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