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Dispersion and fractional Lie group analysis of time fractional equation from Burgers hierarchy
Bikramjeet Kaur,R.K. Gupta
Keywords:Fractional differential equations, Symmetry analysis, Explicit solutions, Dispersion, Conservation laws.
Abstract:
      The paper presents the analysis of time fractional $5^{th}$ order equation 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 infinitesimal symmetries to obtain nonlinear fractional ordinary differential equations having Erd$\acute{e}$lyi-Kober fractional differential operator. The explicit power series solution is obtained for reduced fractional ordinary differential equation and its convergence is discussed. The solution is appeared in the form of singular kink wave and further analysed graphically for various values of fractional order $\alpha$. The new conservation theorem is applied to derive the conservation laws.