  The analysis of a dynamical system modelled by differential (continuum case)
or difference equation (discrete case) with deformed exponential decay, here we
consider Tsallis and Kaniadakis exponentials, may require the use of the
recently proposed deformed Lambert functions: the Lambert-Tsallis and
Lambert-Kaniadakis functions. In this direction, the present work studies the
logistic map with deformed exponential decay, using the Lambert-Tsallis and the
Lambert-Kaniadakis functions to determine the stable behaviour and the dynamic
of the disentropy in the weak chaotic regime. Furthermore, we investigate the
motion of projectile when the vertical motion is governed by a non-linear
differential equation with Tsallis exponential in the coefficient of the second
order derivative. In this case, we calculated the range of the projectile using
the Lambert-Tsallis function.
