Applications of Ea as a substitute for the exponential in other domains

Determine whether the new Mittag-Leffler-type function Ea can replace the exponential function in other areas, including the construction of probability distributions (e.g., a Poisson-type distribution) and the study of PDEs with exponential terms such as the heat equation.

Background

Because Ea generalizes exponential behavior in the L-fractional context, leveraging it in probability and PDEs could yield new models and analytical tools mirroring classical exponential-based theory.