A new characteristic property of the Mittag-Leffler function with 1 < α < 2 is deduced. Motivated by this property, a new notion, named α-order cosine function, is developed. It is proved that an α-order cosine function is associated with a solution operator of an α-order abstract Cauchy problem. Consequently, an α-order abstract Cauchy problem is well-posed if and only if its coefficient operator generates a unique α-order cosine function.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm220-2-2,
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},
volume = {223},
year = {2014},
pages = {119-140},
zbl = {1297.33015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm220-2-2}
}
Zhan-Dong Mei; Ji-Gen Peng; Jun-Xiong Jia. A new characteristic property of Mittag-Leffler functions and fractional cosine functions. Studia Mathematica, Tome 223 (2014) pp. 119-140. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm220-2-2/