Lie symmetry analysis, conservation laws and analytic solutions of the time fractional Kolmogorov-Petrovskii-Piskunov equation

In this paper, we consider the invariance properties of the multiple-term fractional Kolmogorov-Petrovskii-Piskunov (FKPP) equation. By employing the Lie symmetry analysis method, we explicitly investigate the vector fields and symmetry reductions of the FKPP equation. Moreover, an effective method is proposed to succinctly derive the exact power series solutions with their convergence analysis of the equation. Finally, by using the new conservation theorem, the conservation laws associated with Lie symmetries of the equation are well constructed with a detailed analysis.