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.

引用

页数：16

共 39 条

[1]

[Anonymous], 2006, THEORY APPL FRACTION

[2]

[Anonymous], 2010, LECT NOTES MATH

[3]

[Anonymous], 2012, FRACTIONAL DYNAMICS

[4]

[Anonymous], 2001, J INTEGR EQUAT APPL, DOI 10.1216/jiea/1020282237

[5]

[Anonymous], 1993, INTRO FRACTIONAL CA

[6]

[Anonymous], 1999, FRACTIONAL DIFFERENT

[7]

[Anonymous], J INTEGRAL EQNS APPL

[8]

[Anonymous], 1981, INTEGRAL SERIES ELEM

[9] EXISTENCE THEOREM FOR ABEL INTEGRAL-EQUATIONS [J].

ATKINSON, KE .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1974, 5 (05) :729-736

[10] On local attractivity of solutions of a functional integral equation of fractional order with deviating arguments [J].

Balachandran, K. ;

Park, J. Y. ;

Julie, M. Diana .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2010, 15 (10) :2809-2817

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