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SCALE-INVARIANT SOLUTION FOR FRACTIONAL ANOMALOUS DIFFUSION EOUATION

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【作者】 Duan Junsheng； Temuer Chaolu；

【Author】 Duan Junsheng Temuer Chaolu (College of Science, Tianjin University of Commerce,Tianjin 300134; College of Science,Inner Mongolia Uiversity of Technology, Huhhot 010062)

【机构】 College of Science Inner Mongolia Uiversity of Technology； Huhhot 010062；

【摘要】 <正>Fractional diffusion equation for transport phenomena in fractal media is an integro-partial differential equation. For solving the problem of this kind of equation the invariants of the group of scaling transformations are given and then used for deriving the integro-ordinary differential equation for the scale-invariant solution. With the help of Mellin transform the scale-invariant solution is obtained in terms of Fox functions. And the series and asymptotic representations for the solution are considered.

【Abstract】 Fractional diffusion equation for transport phenomena in fractal media is an integro-partial differential equation. For solving the problem of this kind of equation the invariants of the group of scaling transformations are given and then used for deriving the integro-ordinary differential equation for the scale-invariant solution. With the help of Mellin transform the scale-invariant solution is obtained in terms of Fox functions. And the series and asymptotic representations for the solution are considered.

【关键词】 fractional calculus； anomalous diffusion； scale-invariant solution； Fox functions；
【Key words】 fractional calculus； anomalous diffusion； scale-invariant solution； Fox functions；
【基金】 Supported by the National Natural Science Foundation of China (10461005);the Department Fund of Science and Technology in Tianjin Higher Education Institutions (20050404).
  • 【文献出处】 Annals of Differential Equations ,微分方程年刊(英文版) , 编辑部邮箱 ,2006年01期
  • 【分类号】O175.2
  • 【被引频次】1
  • 【下载频次】30
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