Similarity solutions to nonlinear heat conduction and Burgers/Korteweg-deVries fractional equations

Authors:
Vladan D. Djordjevic;Teodor M. Atanackovic
Affiliations:
Faculty of Mechanical Engineering, University of Belgrade, 11000 Belgrade, Serbia;Department of Mechanics, University of Novi Sad, 21000 Novi Sad, Serbia
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

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Abstract

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.