Similarity Solution for Fractional Diffusion Equation
Fractional diffusion equation in fractal media is an integropartial differential equation parametrized by fractal Hausdorff dimension and anomalous diffusion exponent. In this paper, the similarity solution of the fractional diffusion equation was considered. Through the invariants of the group of s...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/548126 |
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| author | Jun-Sheng Duan Ai-Ping Guo Wen-Zai Yun |
| author_facet | Jun-Sheng Duan Ai-Ping Guo Wen-Zai Yun |
| author_sort | Jun-Sheng Duan |
| collection | DOAJ |
| description | Fractional diffusion equation in fractal media is an integropartial differential equation parametrized by fractal Hausdorff dimension and anomalous diffusion exponent. In this paper, the similarity solution of the fractional diffusion equation was considered. Through the invariants of the group of scaling transformations we derived the integro-ordinary differential equation for the similarity variable. Then by virtue of Mellin transform, the probability density function p(r,t), which is just the fundamental solution of the fractional diffusion equation, was expressed in terms of Fox functions. |
| format | Article |
| id | doaj-art-47a768633d19418c890b95fa6d594fda |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-47a768633d19418c890b95fa6d594fda2025-02-03T07:25:49ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/548126548126Similarity Solution for Fractional Diffusion EquationJun-Sheng Duan0Ai-Ping Guo1Wen-Zai Yun2School of Sciences, Shanghai Institute of Technology, Shanghai 201418, ChinaSchool of Mathematics, Baotou Teachers College, Baotou, Inner Mongolia 014030, ChinaSchool of Mathematics, Baotou Teachers College, Baotou, Inner Mongolia 014030, ChinaFractional diffusion equation in fractal media is an integropartial differential equation parametrized by fractal Hausdorff dimension and anomalous diffusion exponent. In this paper, the similarity solution of the fractional diffusion equation was considered. Through the invariants of the group of scaling transformations we derived the integro-ordinary differential equation for the similarity variable. Then by virtue of Mellin transform, the probability density function p(r,t), which is just the fundamental solution of the fractional diffusion equation, was expressed in terms of Fox functions.http://dx.doi.org/10.1155/2014/548126 |
| spellingShingle | Jun-Sheng Duan Ai-Ping Guo Wen-Zai Yun Similarity Solution for Fractional Diffusion Equation Abstract and Applied Analysis |
| title | Similarity Solution for Fractional Diffusion Equation |
| title_full | Similarity Solution for Fractional Diffusion Equation |
| title_fullStr | Similarity Solution for Fractional Diffusion Equation |
| title_full_unstemmed | Similarity Solution for Fractional Diffusion Equation |
| title_short | Similarity Solution for Fractional Diffusion Equation |
| title_sort | similarity solution for fractional diffusion equation |
| url | http://dx.doi.org/10.1155/2014/548126 |
| work_keys_str_mv | AT junshengduan similaritysolutionforfractionaldiffusionequation AT aipingguo similaritysolutionforfractionaldiffusionequation AT wenzaiyun similaritysolutionforfractionaldiffusionequation |