Symmetry analysis, optimal system, conservation laws and exact solutions of time-fractional diffusion-type equation

Abstract

In Liu et al. [On the generalized time fractional diffusion equation: Symmetry analysis, conservation laws, optimal system and exact solutions, Int. J. Geom. Methods Mod. Phys. 17(01) (2020) 2050013], the generalized time-fractional diffusion equation [Formula: see text] is studied by the symmetry analysis method. Liu et al. obtained two group generators [Formula: see text] [Formula: see text] and only one trivial solution [Formula: see text] for the equation. In this paper, we classify the Lie symmetry group admitted by the equation, and for the case [Formula: see text], we obtain a richer set of group generators and some nontrivial solutions, including unprecedented exact solutions and power series solutions. In addition, we construct the one-dimensional optimal system of the Lie symmetry group admitted by the time-fractional diffusion-type equation by Olver’s method, and obtain the conservation laws for all the obtained Lie symmetries using the general method developed by Ibragimov. For the novel exact solutions and power series solutions, we analyze their dynamic behavior graphically.