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 ( a t α ) E α ( a s α ) , t , s ⩾ 0 , where a is a real constant and α > 0 . In this note i...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2010-10, Vol.370 (2), p.635-638
Main Authors: Peng, Jigen, Li, Kexue
Format: Article
Language:English
Subjects:
Caputo's fractional derivative
Exact sciences and technology
Group theory
Group theory and generalizations
Laplace transform
Mathematical analysis
Mathematics
Mittag-Leffler function
Real functions
Sciences and techniques of general use
Semigroup property
Special functions
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Summary: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 ( a t α ) E α ( a s 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 E α ( a t α ) is developed, whose limit state as α ↑ 1 is just the property (0.1).
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2010.04.031