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.

引用

页码：119 / 140

页数：22

共 17 条

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