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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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/567401 |
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| _version_ | 1832556413602234368 |
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| author | Ming-Sheng Hu Ravi P. Agarwal Xiao-Jun Yang |
| author_facet | Ming-Sheng Hu Ravi P. Agarwal Xiao-Jun Yang |
| author_sort | Ming-Sheng Hu |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-da962e5d9d8c4ffc8664f06017252136 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-da962e5d9d8c4ffc8664f060172521362025-02-03T05:45:34ZengWileyAbstract 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 |
| 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 |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2012/567401 |
| work_keys_str_mv | AT mingshenghu localfractionalfourierserieswithapplicationtowaveequationinfractalvibratingstring AT ravipagarwal localfractionalfourierserieswithapplicationtowaveequationinfractalvibratingstring AT xiaojunyang localfractionalfourierserieswithapplicationtowaveequationinfractalvibratingstring |