A note on property of the Mittag-Leffler function

作者：Peng, Jigen^*; Li, Kexue

来源：Journal of Mathematical Analysis and Applications, 2010, 370(2): 635-638.

DOI：10.1016/j.jmaa.2010.04.031

• Mittag-Leffier function
• Caputo's fractional derivative
• Semigroup property
• Laplace transform

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.
E alpha (a(t + s)(alpha)) = E(alpha) (at(alpha)) E(alpha) (as(alpha)) t, s >= 0, (0.1)
where a is a real constant and alpha > 0. In this note it is proved that the above property is unavailable unless alpha = 1 or a = 0. Moreover, a new equality on E(alpha) (at(alpha)) is developed, whose limit state as alpha up arrow 1 is just the property (0.1).

• 出版日期2010-10-15
• 单位西安交通大学