  Proper modeling of complex systems requires innovative mathematical tools. In
this sense, we sought to use deformed or fractal derivatives for studying the
dynamics of systems, particularly those, such as granular gases, in which the
description of the dynamics can be done by using the stretched exponential
probability densities. In this contribution we draw up three results of this
application of mathematical tools. The first result shows that when we use
constraints with finite momentum and the principle of maximum entropy, the
Kohlrausch--Williams--Watts function, known as stretched exponential, emerges
naturally and in a simpler way, when compared to results in the literature.
Next, we obtain generalized expressions for the Langevin equation, as well as
its solutions for three different deformed derivatives, including those
connected with nonaddictive statistical mechanics. The Haff's-like law for
granular gases are obtained. Next, we calculate the partition function $Z$ for
a granular gas system by building up the probability density in terms of the
stretched exponential function. From this partition function, we determine the
internal energy of the system as well as the specific heat, both dependent on
temperature. The consistency with classical approach of kinetic theory for
ideal gases was verified.
