This paper address a new vision for the generalized Mittag-Leffler stability of the fractional differential equations. We mainly focus on a new method, consisting of decomposing a given fractional differential equation into a cascade of many sub-fractional differential equations. And we propose a procedure for analyzing the generalized Mittag-Leffler stability for the given fractional different...

Atomic cascades are ubiquitous in nature and they have been explored within very different scenarios, from precision measurements to the modeling of astrophysical spectra, up radiation damage biological matter. However, present, a quantitative analysis these often failed because their inherent complexity. Apart utilizing rotational symmetry atoms proper distinction physical schemes, hierarchy u...