2014/08/28 by Nelson H. T. Lemes, José Paulo Carvalho dos Santos, José Paulo C. dos Santos +2 · 18 citations
Chemistry · Mathematics · Physics and Astronomy · #Applied mathematics #Calculus (dental) #Computer science #Differential equation #Exponential function #Fractional Differential Equations Solutions #Fractional calculus #Function (biology) #Mathematical analysis #Mathematics #Mittag-Leffler function #Physics #Process (computing) #Quantum mechanics #Series (stratigraphy) #Spectroscopy and Quantum Chemical Studies #Statistical physics #Statistics #Stochastic process #Work (physics) #cond-mat.stat-mech #thermodynamics and calorimetric analyses
paper · pdf · doi:10.1016/j.apm.2016.04.021
published in Applied Mathematical Modelling 40(17-18), 7971-7976 (Elsevier BV) · 12 pages, 2 figures
arxiv created 2014/08/28 · openalex publication_date 2016/05/06 · openalex created_date 2016/06/24 · arxiv updated 2016/07/05 · openalex updated_date 2026/08/05
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.