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

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

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 scient...

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Main Authors: Ming-Sheng Hu, Ravi P. Agarwal, Xiao-Jun Yang
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2012/567401
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spelling doaj-da962e5d9d8c4ffc8664f060172521362020-11-24T20:58:03ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/567401567401Local Fractional Fourier Series with Application to Wave Equation in Fractal Vibrating StringMing-Sheng Hu0Ravi P. Agarwal1Xiao-Jun Yang2Institute of Software Science, Zhengzhou Normal University, Zhengzhou 450044, ChinaDepartment of Mathematics, Texas A and M University, Kingsville, TX 78363-8202, USADepartment of Mathematics and Mechanics, China University of Mining and Technology, Jiangsu, Xuzhou 221008, ChinaWe 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.http://dx.doi.org/10.1155/2012/567401
collection DOAJ
language English
format Article
sources DOAJ
author Ming-Sheng Hu
Ravi P. Agarwal
Xiao-Jun Yang
spellingShingle Ming-Sheng Hu
Ravi P. Agarwal
Xiao-Jun Yang
Local Fractional Fourier Series with Application to Wave Equation in Fractal Vibrating String
Abstract and Applied Analysis
author_facet Ming-Sheng Hu
Ravi P. Agarwal
Xiao-Jun Yang
author_sort Ming-Sheng Hu
title Local Fractional Fourier Series with Application to Wave Equation in Fractal Vibrating String
title_short Local Fractional Fourier Series with Application to Wave Equation in Fractal Vibrating String
title_full Local Fractional Fourier Series with Application to Wave Equation in Fractal Vibrating String
title_fullStr Local Fractional Fourier Series with Application to Wave Equation in Fractal Vibrating String
title_full_unstemmed Local Fractional Fourier Series with Application to Wave Equation in Fractal Vibrating String
title_sort local fractional fourier series with application to wave equation in fractal vibrating string
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2012-01-01
description 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.
url http://dx.doi.org/10.1155/2012/567401
work_keys_str_mv AT mingshenghu localfractionalfourierserieswithapplicationtowaveequationinfractalvibratingstring
AT ravipagarwal localfractionalfourierserieswithapplicationtowaveequationinfractalvibratingstring
AT xiaojunyang localfractionalfourierserieswithapplicationtowaveequationinfractalvibratingstring
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