Deformable exponentials are used in different domains, for instance in statistics or thermodynamics. Since they are a useful mathematical tool, this paper deals with the presentation of deformable exponential functions with increasing or decreasing evolutions with respect to the deformation coefficient. Deformable exponential functions with one or two variables are presented, with applications in modeling propagation phenomena. Some examples are provided to emphasize the deformation among the propagation process, data tables and figures, obtained by means of numerical simulations.