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

Boundary value problems

Michal Fekan¹  Chun Zhu¹  JinRong Wang² 

[1] Department of Mathematics, Guizhou University, Guiyang, P.R. China;School of Mathematics and Computer Science, Guizhou Normal College, Guiyang, P.R. China

关键词: Abel-type nonlinear integral equations;    weakly singular kernels;    existence;    numerical solutions;   

DOI  :  10.1186/1687-2770-2014-20

学科分类：数学（综合）

来源: SpringerOpen

【 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. MSC:26A33, 45E10, 45G05.

【 授权许可】

CC BY