  We analyse the dynamics of the Warsaw Stock Exchange index WIG at a daily
time horizon before and after its well defined local maxima of the cusp-like
shape decorated with oscillations. The rising and falling paths of the index
peaks can be described by the Mittag-Leffler function superposed with various
types of oscillations. The latter is a solution of our model of index dynamics
defined by the nonhomogeneous fractional relaxation equation. This solution is
a generalised analog of an exactly solvable model of viscoelastic materials. We
found that the Warsaw Stock Exchange can be considered as an intermediate
system lying between two complex ones, defined by short and long-time limits of
the Mittag-Leffler function; these limits are given by the
Kohlraush-Williams-Watts law for the initial times, and the power-law or the
Nutting law for asymptotic time. Hence follows the corresponding short- and
long-time power-law behaviour (different universality classes) of the
time-derivative of the logarithm of WIG which can in fact be viewed as the
finger print of a dynamical critical phenomenon.
