A FRACTIONAL CALCULUS APPROACH TO INVESTIGATE THE ALPHA DECAY PROCESSES

Abstract

In this study, the nuclear decay equation is taken under consideration by making use of fractional calculus. In this context, the first-order time derivative is changed to a Caputo fractional derivative hence, the resulting equation is the time fractional nuclear decay equation. The solution of this equation is obtained in terms of Mittag–Leffler function which plays an important role to study the non-Markovian feature of physical processes. As an application of this time fractional formalism, alpha decay half-life values have been calculated for Pb , Po , Rn , Ra , Th and U isotopes. Consequently, the theoretical half-life values have been obtained in consistent with the experimental data. The dependence of the order of fractional derivative μ being a measure of fractality of time, on the nuclear structure has been established. In the investigations carried out, we have arrived to the conclusion that for the μ values which are closed to one, where time becomes homogenous and continuous, the shell closure effects are predominant and that the fractional derivative order μ (i.e., fractality of time) and nuclear structure are closely related to each other.