Lie symmetry analysis, explicit solutions and conservation laws for the time fractional Kolmogorov–Petrovskii–Piskunov equation

Abstract

ABSTRACT In this paper, Lie symmetry method is applied to investigate the invariance properties of the time fractional Kolmogorov–Petrovskii–Piskunov equation with Riemann–Liouville derivative. In view of point symmetry, the vector fields for the governing equation are well constructed. And then the equation can be reduced to a fractional ODE with the help of Erdélyi–Kober operator. Moreover, a kind of explicit power series solutions of the equation is derived by virtue of the power series theory. Lastly, based on Ibragimov's method, two kinds of conservation laws for the equation are established.