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

[1] Spectral analysis of fractional kinetic equations with random data
Anh, VV
Leonenko, NN
[J]. JOURNAL OF STATISTICAL PHYSICS, 2001, 104 (5-6) : 1349 - 1387
[2] [Anonymous], 2006, THEORY APPL FRACTION, DOI DOI 10.1016/S0304-0208(06)80001-0
[3] [Anonymous], 2000, Applications of Fractional Calculus in Physics
[4] [Anonymous], 1955, HIGHER TRANSCENDENTA
[5] [Anonymous], 1999, FRACTIONAL DIFFERENT
[6] [Anonymous], 2001, FRACTIONAL EVOLUTION
[7] ARENDT W, 2001, MONOGR MATH, V96
[8] On fractional resolvent operator functions
Chen, Chuang
Li, Miao
[J]. SEMIGROUP FORUM, 2010, 80 (01) : 121 - 142
[9] Cauchy problem for fractional diffusion equations
Eidelman, SD
Kochubei, AN
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2004, 199 (02) : 211 - 255
[10] Goldstein J. A., 1985, SEMIGROUPS LINEAR OP

← 1 2 →