Lie Group Analysis and Invariant Solutions for Nonlinear Time-Fractional Diffusion-Convection Equations*

On the basis of Lie group theory, (1 + N)-dimensional time-fractional partial differential equations are studied and the expression of is given. As applications, two special forms of nonlinear time-fractional diffusion-convection equations are investigated by Lie group analysis method. Then the equations are reduced into fractional ordinary differential equations under group transformations. Therefore, the invariant solutions and some exact solutions are obtained.