Symmetry analysis for time-fractional convection-diffusion equation

Abstract

The time-fractional convection-diffusion equation is performed by Lie symmetry analysis method which involves the Riemann-Liouville time-fractional derivative of the order $\alpha\in(0,2)$. In eight cases, the symmetries are obtained and similarity reductions of the equation are deduced by means of symmetry. It is shown that the fractional equation can be reduced into fractional ordinary differential equations. Some group invariant solutions in explicit form are obtained in some cases.