On group invariant solutions of fractional order Burgers-Poisson equation

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 α and β, 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.