Beer-Lambert law in photochemistry: A new approach

Obtaining a reliable formulation of the Beer-Lambert law in photochemistry requires knowledge on the role that the space-time dependence of the absorbance plays on the system. Spatial memory due to correlation between obstacles can be modeled, among other methods, by using a fractional calculus approach. Here we present a generalized Beer-Lambert law, based on Mittag-Leffler extinction of radiation, which is derived through probabilistic arguments, by assuming that the number of extinction events follows a fractional Poisson distribution. We applied such an approach in photochemistry by using a mathematical model that involves fractional derivative with respect to another function that accounts for the role of both space-dependence of the absorbance and spatial memory. We finally provide a discussion of the utility and implications of this new approach.