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Open AccessArticle

Towards a Generalized Beer-Lambert Law

Institute of Atmospheric Science and Climate, Italian National Research Council (CNR), 00133 Rome, Italy
Dipartimento di Scienze Statistiche, “Sapienza” Università di Roma, 00185 Rome, Italy
Author to whom correspondence should be addressed.
Fractal Fract 2018, 2(1), 8;
Received: 31 December 2017 / Revised: 26 January 2018 / Accepted: 27 January 2018 / Published: 31 January 2018
(This article belongs to the Special Issue Fractional Dynamics)
Anomalous deviations from the Beer-Lambert law have been observed for a long time in a wide range of application. Despite all the attempts, a reliable and accepted model has not been provided so far. In addition, in some cases the attenuation of radiation seems to follow a hyperbolic more than an exponential extinction law. Starting from a probabilistic interpretation of the Beer-Lambert law based on Poissonian distribution of extinction events, in this paper we consider deviations from the classical exponential extinction introducing a weighted version of the classical law. The generalized law is able to account for both sub or super-exponential extinction of radiation, and can be extended to the case of inhomogeneous media. Focusing on this case, we consider a generalized Beer-Lambert law based on an inhomogeneous weighted Poisson distribution involving a Mittag-Leffler function, and show how it can be directly related to hyperbolic decay laws observed in some applications particularly relevant to microbiology and pharmacology. View Full-Text
Keywords: Beer-Lambert law; hyperbolic extinction; poisson process; fractional calculus Beer-Lambert law; hyperbolic extinction; poisson process; fractional calculus
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Casasanta, G.; Garra, R. Towards a Generalized Beer-Lambert Law. Fractal Fract 2018, 2, 8.

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