期刊
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
卷 222, 期 2, 页码 701-714出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cam.2007.12.013
关键词
Lie-group scaling transformation; Similarity solutions; Fractional heat conduction equation; Fractional Burgers/Korteweg-deVries equation
资金
- Ministry of Science and Environmental Protection of the Republic of Serbia [144022, 144019]
We analyze self-similar Solutions to a nonlinear fractional diffusion equation and fractional Burgers/Korteweg-deVries equation in one spatial variable. By using Lie-group scaling transformation, we determined the similarity Solutions. After the introduction of the similarity variables, both problems are reduced to ordinary nonlinear fractional differential equations. In two special cases exact Solutions to the ordinary fractional differential equation, which is derived from the diffusion equation, are presented. In several other cases the ordinary fractional differential equations are solved numerically, for several values of governing parameters. In formulating the numerical procedure, we use special representation of a fractional derivative that is recently obtained. (C) 2007 Elsevier B.V. All rights reserved.
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