  In this survey paper we consider some applications of the Wright function
with special emphasis of its key role in the partial differential equations of
fractional order. It was found that the Green function of the time-fractional
diffusion-wave equation can be represented in terms of the Wright function.
Furthermore, extending the methods of Lie groups in partial differential
equations to the partial differential equations of fractional order it was
shown that some of the group-invariant solutions of these equations can be
given in terms of the Wright and the generalized Wright functions.Finally, we
discuss recent results about distribution of zeros of the Wright function, its
order, type and indicator function.
