A new characteristic property of Mittag-Leffler functions and fractional cosine functions

Zhan-Dong Mei, Ji-Gen Peng, and Jun-Xiong Jia. "A new characteristic property of Mittag-Leffler functions and fractional cosine functions." Studia Mathematica 220.2 (2014): 119-140. <http://eudml.org/doc/285631>.

@article{Zhan2014,
abstract = {A new characteristic property of the Mittag-Leffler function $E_\{α\}(at^\{α\})$ 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.},
author = {Zhan-Dong Mei, Ji-Gen Peng, Jun-Xiong Jia},
journal = {Studia Mathematica},
keywords = {Mittag-Leffler functions; characteristic property; fractional cosine function; abstract fractional Cauchy problem},
language = {eng},
number = {2},
pages = {119-140},
title = {A new characteristic property of Mittag-Leffler functions and fractional cosine functions},
url = {http://eudml.org/doc/285631},
volume = {220},
year = {2014},
}

TY - JOUR
AU - Zhan-Dong Mei
AU - Ji-Gen Peng
AU - Jun-Xiong Jia
TI - A new characteristic property of Mittag-Leffler functions and fractional cosine functions
JO - Studia Mathematica
PY - 2014
VL - 220
IS - 2
SP - 119
EP - 140
AB - A new characteristic property of the Mittag-Leffler function $E_{α}(at^{α})$ 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.
LA - eng
KW - Mittag-Leffler functions; characteristic property; fractional cosine function; abstract fractional Cauchy problem
UR - http://eudml.org/doc/285631
ER -