A generalized Mittag-Leffer function to describe nonexponential chemical effects

TL;DR

This paper introduces a fractional differential equation model using the Mittag-Leffer function to accurately describe anomalous luminescence decay, capturing both exponential and non-exponential behaviors over different time scales.

Contribution

It presents a novel fractional differential equation approach with an exact solution based on the Mittag-Leffer function for modeling complex decay processes.

Findings

The fractional model accurately fits experimental decay data.

The Mittag-Leffer function captures both short and long-term decay behaviors.

A stochastic analysis supports the fractional calculus framework.

Abstract

In this paper a differential equation with noninteger order was used to model an anomalous luminescence decay process. Although this process is in principle an exponential decaying process, recent data indicates that is not the case for longer observation time. The theoretical fractional differential calculus applied in the present work was able to describe this process at short and long time, explaining, in a single equation, both exponential and non-exponential decay process. The exact solution found by fractional model is given by an infinite serie, the Mittag-Leffer function, with two adjusting parameters. To further illustrate this nonexponential behaviour and the fractional calculus framework, an stochastic analysis is also proposed.