Extremal solutions of Cauchy problems for abstract fractional differential equations

被引：1

作者：

Wang, JinRong ^{[1
]}

Zhou, Yong ^{[2
]}

Medved, Milan ^{[3
]}

机构：

[1] Guizhou Normal Coll, Sch Math & Comp Sci, Guiyang 550018, Guizhou, Peoples R China

[2] Xiangtan Univ, Dept Math, Xiangtan 411105, Hunan, Peoples R China

[3] Comenius Univ, Dept Math & Numer Math, SK-84215 Bratislava, Slovakia

来源：

MATHEMATICA SLOVACA | 2013年 / 63卷 / 04期

基金：

中国国家自然科学基金;

关键词：

fractional differential equations; extremal solutions; existence; fixed point method; INTEGRAL-INEQUALITIES; EVOLUTION-EQUATIONS; EXISTENCE;

D O I：

10.2478/s12175-013-0134-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the extremal solutions of Cauchy problems for abstract fractional differential equations. Some definitions such as L (1)-Lipschitz-like, L (1)-Carath,odory-like and L (1)-Chandrabhan-like are introduced. By virtue of the singular integral inequalities with several nonlinearities due to Medved', the properties of solutions are given. By using a hybrid fixed point theorem due to Dhage, existence results for extremal solutions are established. Finally, we present an example to illustrate our main results.

引用

页码：769 / 792

页数：24

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