A comparative analysis of generalized exponential decay

This paper explores the similarities and differences between the Mittag-Leffler function and a recently introduced one-parameter function, when (α, q) ∈ (0, 1)—where α is called the fractional parameter and q is called the entropic parameter, respectively. We use the half-life of Oxygen-22—an isotope of oxygen—to determine a q-analog of the decay constant. This enabled us to utilize the Tsallis logarithmic function and generate various plots depicting generalized exponential decay. Thereafter, a comparison is made with the Mittag-Leffler function once we establish the fractional analog of the nuclear disintegration law—the fractional radioactive decay law. Hence, we show that when compared to each other, the Mittag-Leffler function generated faster decaying rates in the limiting case when (α, q) → 1.