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：
暂无
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.
引用
收藏
相关论文
共 50 条
[41]   An hp-Version Chebyshev Spectral Collocation Method for Nonlinear Volterra Integro-Differential Equations with Weakly Singular Kernels [J].
Jia, Hongli ;
Yang, Yang ;
Wang, Zhongqing .
NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS, 2019, 12 (03) :969-994
[42]   Galerkin and multi-Galerkin methods for weakly singular Volterra–Hammerstein integral equations and their convergence analysis [J].
Kapil Kant ;
Gnaneshwar Nelakanti .
Computational and Applied Mathematics, 2020, 39
[43]   Smoothing transformation for numerical solution of nonlinear weakly singular Volterra integral equations using quasilinearization and product integration methods [J].
Najafi, Esmaeil .
APPLIED NUMERICAL MATHEMATICS, 2020, 153 :540-557
[44]   On systems of volterra difference equations associated with collocation methods for weakly singular Volterra integral equations [J].
Brunner, H .
NEW DEVELOPMENTS IN DIFFERENCE EQUATIONS AND APPLICATIONS, 1999, :75-92
[45]   A novel Jacob spectral method for multi-dimensional weakly singular nonlinear Volterra integral equations with nonsmooth solutions [J].
Mahmoud A. Zaky ;
Ibrahem G. Ameen .
Engineering with Computers, 2021, 37 :2623-2631
[46]   SOLUTIONS OF SINGULAR INTEGRAL EQUATIONS OF GENERALIZED CONVOLUTION TYPE [J].
Nagdy, Abbas Sedky ;
Hashem, Khaled Mahmoud .
TRANSACTIONS OF A RAZMADZE MATHEMATICAL INSTITUTE, 2025, 179 (01) :147-155
[47]   Generalized convolution-type singular integral equations [J].
Li, Pingrun .
APPLIED MATHEMATICS AND COMPUTATION, 2017, 311 :314-323
[48]   Tau approximation method for the weakly singular Volterra-Hammerstein integral equations [J].
Ahmadabadi, M. Nili ;
Dastjerdi, H. Laeli .
APPLIED MATHEMATICS AND COMPUTATION, 2016, 285 :241-247
[49]   Uniqueness of solutions to an Abel type nonlinear integral equation on the half line [J].
Mydlarczyk, Wojciech .
CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, 2012, 10 (06) :1995-2002
[50]   Legendre Spectral Projection Methods for Hammerstein Integral Equations with Weakly Singular Kernel [J].
Panigrahi B.L. .
International Journal of Applied and Computational Mathematics, 2018, 4 (6)
12345