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

Source: arXiv

ABSTRACT 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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    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 · 1.60 Impact Factor

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Sep 9, 2014