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

被引：6
|
作者：
Mei, Zhan-Dong [1 ]
Peng, Ji-Gen [1 ]
Jia, Jun-Xiong [1 ]
机构：
[1] Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Peoples R China
来源：
STUDIA MATHEMATICA | 2014年 / 220卷 / 02期
基金：
高等学校博士学科点专项科研基金;
关键词：
Mittag-Leffler function; fractional abstract Cauchy problem; fractional cosine function; CAUCHY-PROBLEM; EQUATIONS;
D O I：
10.4064/sm220-2-2
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
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页码：119 / 140
页数：22
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