Investigation of alpha decay by using fractional calculus

In this study, the nuclear decay equation has been taken again under consideration of the nuclear decay equation fractional calculus. In this context, a Caputo fractional derivative operator has been performed instead of the first order time derivative operator. Hence, the resulting new equation converts to the time fractional nuclear decay equation. The solution of this new equation has been obtained in terms of Mittag-Leffler function. 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. In the literature, a corrected factor has been used in order to make the equivalent experimental and theoretical half-life values. However, the fractional half-life values in the present study, have been obtained in consistent with the experimental data. Consequently, the fractional derivative order and nuclear structure have been concluded closely related to each other.