Abstract and Applied Analysis
Volume 2012 (2012), Article ID 567401, 15 pages
http://dx.doi.org/10.1155/2012/567401
Research Article

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

Ming-Sheng Hu,1 Ravi P. Agarwal,2 and Xiao-Jun Yang3

1Institute of Software Science, Zhengzhou Normal University, Zhengzhou 450044, China
2Department of Mathematics, Texas A and M University, Kingsville, TX 78363-8202, USA
3Department of Mathematics and Mechanics, China University of Mining and Technology, Jiangsu, Xuzhou 221008, China

Received 14 August 2012; Revised 25 October 2012; Accepted 8 November 2012

Academic Editor: Lan Xu

Copyright © 2012 Ming-Sheng Hu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.