Analysis of Abel-type nonlinear integral equations with weakly singular kernels

被引：9
|
作者：
Wang, JinRong [1 ,2 ]
Zhu, Chun [2 ]
Feckan, Michal [3 ,4 ]
机构：
[1] Guizhou Normal Coll, Sch Math & Comp Sci, Guiyang 550018, Guizhou, Peoples R China
[2] Guizhou Univ, Dept Math, Guiyang 550025, Guizhou, Peoples R China
[3] Comenius Univ, Dept Math Anal & Numer Math, Bratislava 84248, Slovakia
[4] Slovak Acad Sci, Inst Math, Bratislava 81473, Slovakia
来源：
BOUNDARY VALUE PROBLEMS | 2014年
基金：
中国国家自然科学基金;
关键词：
Abel-type nonlinear integral equations; weakly singular kernels; existence; numerical solutions; LOCAL ATTRACTIVITY; FRACTIONAL ORDER; EXISTENCE;
D O I：
10.1186/1687-2770-2014-20
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we investigate Abel-type nonlinear integral equations with weakly singular kernels. Existence and uniqueness of nontrivial solution are presented in an order interval of a cone by using fixed point methods. As a byproduct of our method, we improve a gap in the proof of Theorem 5 in Buckwar (Nonlinear Anal. TMA 63: 88-96, 2005). As an extension, solutions in closed form of some Erdelyi-Kober-type fractional integral equations are given. Finally theoretical results with three illustrative examples are presented.
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页数：16
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