Dispersion and fractional lie group analysis of time fractional equation from burgers hierarchy

Abstract

The paper presents the analysis of time fractional 5th order equa tion from Burgers hierarchy. We discuss the dispersion relation and provide the complete analysis of the phase velocity and group velocity along with the nature of wave dispersion. Similarity reductions are carried out using innites imal symmetries to obtain nonlinear fractional ordinary di erential equations having Erdelyi-Kober fractional di erential operator. The explicit power se ries solution is obtained for reduced fractional ordinary di erential equation and its convergence is discussed. The solution is appeared in the form of singu lar kink wave and further analysed graphically for various values of fractional order . The new conservation theorem is applied to derive the conservation laws.