On the properties of a Cauchy-type problem for an abstract differential equation with fractional derivatives

被引：7

作者：

Glushak, A. V. ^{[1
]}

机构：

[1] Belgorod State Univ, Belgorod, Russia

来源：

MATHEMATICAL NOTES | 2007年 / 82卷 / 5-6期

基金：

俄罗斯基础研究基金会;

关键词：

differential equation with fractional derivatives; Cauchy-type problem; Riemann-Lionville fractional derivative; fractional integral; Mittag-Leffler function;

D O I：

10.1134/S000143460711003X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We Study the relationship between the Solutions of abstract differential equations with fractional derivatives and their stability with respect to the perturbation by a bounded operator. Besides, we obtain representations for the solution of an inhomogeneous equation and for an equation containing a fractional power of the generator of a cosine operator function.

引用

页码：596 / 607

页数：12

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