Symmetry structure of multi-dimensional time-fractional partial differential equations

In this paper, we concentrate on the Lie symmetry structure of a system of multi-dimensional time-fractional partial differential equations (PDEs). Specifically, we first give an explicit prolongation formula involving Riemann-Liouville time-fractional derivative for the Lie infinitesimal generator in multi-dimensional case, and then show that the infinitesimal generator has an elegant structure. Furthermore, we present two simple conditions to determine the infinitesimal generators where one is a system of linear time-fractional PDEs, the other is a system of integer-order PDEs and plays the dominant role in finding the infinitesimal generators. We study three time-fractional PDEs to illustrate the efficiencies of the results.