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
收藏
页数：16
相关论文
共 50 条
  • [1] Analysis of Abel-type nonlinear integral equations with weakly singular kernels
    JinRong Wang
    Chun Zhu
    Michal Fečkan
    Boundary Value Problems, 2014
  • [2] On Multi-Singular Integral Equations Involving n Weakly Singular Kernels
    Sales, S. M. S. Nabavi
    Baghani, O.
    FILOMAT, 2018, 32 (04) : 1323 - 1333
  • [3] Matrix Method by Genocchi Polynomials for Solving Nonlinear Volterra Integral Equations with Weakly Singular Kernels
    Hashemizadeh, Elham
    Ebadi, Mohammad Ali
    Noeiaghdam, Samad
    SYMMETRY-BASEL, 2020, 12 (12): : 1 - 19
  • [4] Spectral approximated superconvergent method for nonlinear Volterra Hammerstein integral equations with weakly singular kernels
    Chakraborty, Samiran
    Agrawal, Shivam Kumar
    Nelakanti, Gnaneshwar
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2025, 467
  • [5] An adaptive Huber method for nonlinear systems of Volterra integral equations with weakly singular kernels and solutions
    Bieniasz, L. K.
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2017, 323 : 136 - 146
  • [6] A hybrid collocation method for Volterra integral equations with weakly singular kernels
    Cao, YZ
    Herdman, T
    Xu, YH
    SIAM JOURNAL ON NUMERICAL ANALYSIS, 2003, 41 (01) : 364 - 381
  • [7] On the numerical solution of integral equations of the second kind with weakly singular kernels
    M. H. Fahmy
    M. A. Abdou
    M. A. Darwish
    Korean Journal of Computational & Applied Mathematics, 1999, 6 (2): : 401 - 409
  • [8] A comprehensive analysis for weakly singular nonlinear functional Volterra integral equations using discretization techniques
    Bhat, Imtiyaz Ahmad
    Mishra, Lakshmi Narayan
    Mishra, Vishnu Narayan
    Abdel-Aty, Mahmoud
    Qasymeh, Montasir
    ALEXANDRIA ENGINEERING JOURNAL, 2024, 104 : 564 - 575
  • [9] On a weakly singular quadratic integral equations of Volterra type in Banach algebras
    Yu, Xiulan
    Zhu, Chun
    Wang, JinRong
    ADVANCES IN DIFFERENCE EQUATIONS, 2014,
  • [10] Discrete Legendre spectral methods for Hammerstein type weakly singular nonlinear Fredholm integral equations
    Mandal, Moumita
    Kant, Kapil
    Nelakanti, Gnaneshwar
    INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2021, 98 (11) : 2251 - 2267
12345