A new characteristic property of Mittag-Leffler functions and fractional cosine functions
Studia Mathematica, Tome 220 (2014) no. 2, pp. 119-140
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
A new characteristic property of the Mittag-Leffler function $E_\alpha (at^\alpha )$ with $1\alpha 2$ is deduced. Motivated by this property, a new notion, named $\alpha $-order cosine function, is developed. It is proved that an $\alpha $-order cosine function is associated with a solution operator of an $\alpha $-order abstract Cauchy problem. Consequently, an $\alpha $-order abstract Cauchy problem is well-posed if and only if its coefficient operator generates a unique $\alpha $-order cosine function.
Keywords:
characteristic property mittag leffler function alpha alpha alpha deduced motivated property notion named alpha order cosine function developed proved alpha order cosine function associated solution operator alpha order abstract cauchy problem consequently alpha order abstract cauchy problem well posed only its coefficient operator generates unique alpha order cosine function
Affiliations des auteurs :
Zhan-Dong Mei 1 ; Ji-Gen Peng 1 ; Jun-Xiong Jia 1
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author = {Zhan-Dong Mei and Ji-Gen Peng and Jun-Xiong Jia},
title = {A new characteristic property of {Mittag-Leffler} functions and fractional cosine functions},
journal = {Studia Mathematica},
pages = {119--140},
publisher = {mathdoc},
volume = {220},
number = {2},
year = {2014},
doi = {10.4064/sm220-2-2},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm220-2-2/}
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Zhan-Dong Mei; Ji-Gen Peng; Jun-Xiong Jia. A new characteristic property of Mittag-Leffler functions and fractional cosine functions. Studia Mathematica, Tome 220 (2014) no. 2, pp. 119-140. doi: 10.4064/sm220-2-2
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