A note on property of the Mittag-Leffler function

Recently the authors have found in some publications that the following property (0.1) of Mittag-Leffler function is taken for granted and used to derive other properties.(0.1)E_α(a(t+s)^α)=E_α(at^α)E_α(as^α),t,s≥0, where a is a real constant and α>0. In this note it is proved that the above property is unavailable unless α=1 or a=0. Moreover, a new equality on Eα(at^α) is developed, whose limit state as α↑1 is just the property (0.1).