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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 of the Lie
infinitesimal generator involving time-fractional partial derivative in
multi-dimensional case, and then show that the admitted infinitesimal generator
has an elegant structure. Furthermore, we present two simple conditions to
determine the infinitesimal generator 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 the whole procedure. We study three time-fractional PDEs to
illustrate the efficiency of the results