Numerical solutions of space-fractional advection-diffusion equation with a source term

A space-fractional advection-diffusion equation, involving the Riemann-Liouville derivative, with a nonlinear source term is considered. The authors determine the Lie symmetries and reduce the original fractional partial differential equation into a fractional ordinary differential equation (FODE), in some interesting cases. Numerical solutions of FODEs are obtained, and through Lie transformations, numerical solutions of original equation are found.The original version of this article supplied to AIP Publishing contained an error in the title. The original version was titled “Numerical solutions of space-fractional advection-diffusion equation with a nonlinear source term.” At the request of all the authors the title has been changed to “Numerical solutions of spacefractional advection-diffusion equation with a source term.” The authors modified the title to better reflect the final results reported in the paper. The updated version of this paper was published on 8 August 2019.