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

被引：0
作者：
JinRong Wang
Chun Zhu
Michal Fečkan
机构：
[1] Guizhou Normal College,School of Mathematics and Computer Science
[2] Guizhou University,Department of Mathematics
[3] Comenius University,Department of Mathematical Analysis and Numerical Mathematics
[4] Slovak Academy of Sciences,Mathematical Institute
来源：
Boundary Value Problems | / 2014卷
关键词：
Abel-type nonlinear integral equations; weakly singular kernels; existence; numerical solutions;
D O I：
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中图分类号：
学科分类号：
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 Erdélyi-Kober-type fractional integral equations are given. Finally theoretical results with three illustrative examples are presented.
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