  We study a class of nonlinear evolution systems of time fractional partial
differential equations using Lie symmetry analysis. We obtain not only
infinitesimal symmetries but also a complete group classification and a
classification of group invariant solutions of this class of systems. We find
that the class of systems of differential equations studied is naturally
divided into two cases on the basis of the type of a function that they
contain. In each case, the dimension of the Lie algebra generated by the
infinitesimal symmetries is greater than 2, and for this reason we present the
structures and one-dimensional optimal systems of these Lie algebras. The
reduced systems corresponding to the optimal systems are also obtained.
Explicit group invariant solutions are found for particular cases.
