Lie group classifications and exact solutions for time-fractional Burgers equation

Source: arXiv


Lie group method provides an efficient tool to solve nonlinear partial differential equations. This paper suggests a fractional Lie group method for fractional partial differential equations. A time-fractional Burgers equation is used as an example to illustrate the effectiveness of the Lie group method and some classes of exact solutions are obtained. Comment: 9 pp, accepted

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Available from: Guo-Cheng Wu, Sep 09, 2014
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    • "The Boussinesq-like equations have been studied by many authors. Zhu [9] discussed some exact special solutions with solitary patterns and Yan [10] derived some new similarity reductions and compacton solutions for Boussinesq-like equations. The main objective of the paper is to obtain approximate solution of the time-fractional Boussinesq-like equation with the FVIM. "

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    ABSTRACT: In this paper, symmetry property of fractional order (space-time) Burgers-Poisson (FBP) equation is investigated. The equation is obtained by replacing first order time and space derivatives to the corresponding fractional derivatives of order alpha and beta, respectively, in the classical Burgers-Poisson equation. We present Lie symmetries and corresponding infinitesimal generators for the FBP equation by using fractional Lie group method. With the help of these infinitesimal generators some group invariant solutions are sought by reducing the order of the equation.
    Applied Mathematics and Computation 10/2014; 244:870-877. DOI:10.1016/j.amc.2014.07.053 · 1.55 Impact Factor