Integral solution of a class of nonlinear integral equations

Liang, Jin; Yan, Sheng-Hua; Agarwal, Ravi P.; Huang, Tingwen

doi:10.1016/j.amc.2012.10.099

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction3

Discussion1

Definition1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2014

2022

Publication Types

Select...

Article8

Relationship

Self Cite0

Independent8

Authors

Journals

Cited by 9 publications

(5 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…By using Egoroff's theorem, we have replaced this method so that the proof process is simplified. The reader can compare it with [5,8,10,21,22].…”

Section: Discussionmentioning

confidence: 99%

Existence of weak solutions for a boundary value problem of a second order ordinary differential equation

Weng

Wang

2018

Bound Value Probl

View full text Add to dashboard Cite

show abstract

“…By using Egoroff's theorem, we have replaced this method so that the proof process is simplified. The reader can compare it with [5,8,10,21,22].…”

Section: Discussionmentioning

confidence: 99%

Existence of weak solutions for a boundary value problem of a second order ordinary differential equation

Weng

Wang

2018

Bound Value Probl

View full text Add to dashboard Cite

show abstract

“…Baleanu and R.P. Agarwal [17], R.P. Agarwal, M. Benchohra, S. Hamani [18], P. Chen, Y. Li and H. Fan [19], Wahash-Panchal-Abdo [40], Ardjounia-Djoudi [41], etc.…”

Section: Introductionmentioning

confidence: 99%

Existence of mild solutions to semilinear fractional evolution equation using Krasnoselskii fixed point theorem

Ngoc

Tuấn

2022

Filomat

View full text Add to dashboard Cite

This paper is devoted to study the existence and stability of mild solutions for semilinear fractional evolution equations with a nonlocal final condition. The analysis is based on analytic semigroup theory, Krasnoselskii fixed point theorem, and a special probability density function. An application to a time fractional diffusion equation with nonlocal final condition is also given.

show abstract

“…At the first moment, we establish a result on the existence and uniqueness of solutions of (1.1) in the function space L 2 (a, b), whose proof is based on the Banach Fixed Point Theorem. Some authors established criteria for the existence of solutions of nonlinear functional integral equation in Banach spaces by using basic fixed point theorems, such as [8,10,11,12,13], for instance. However, the conditions about existence and uniqueness were used depending on the Carathéodorytype conditions of the kernel, which are not required in this work.…”

Section: Introductionmentioning

confidence: 99%

Numerical Analysis of the Chebyshev Collocation Method for Functional Volterra Integral Equations

Azevedo

Afonso

Silva

2020

Tend. Mat. Apl. Comput.

View full text Add to dashboard Cite

The collocation method based on Chebyshev basis functions, coupled Picard iterative process, is proposed to solve a functional Volterra integral equation of the second kind. Using the Banach Fixed Point Theorem, we prove theorems on the existence and uniqueness solutions in the L2-norm. We also provide the convergence and stability analysis of the proposed method, which indicates that the numerical errors in the L2-norm decay exponentially, provided that the kernel function is sufficiently smooth. Numerical results are presented and they confirm the theoretical prediction of the exponential rate of convergence.

show abstract

Integral solution of a class of nonlinear integral equations

Cited by 9 publications

References 21 publications

Existence of weak solutions for a boundary value problem of a second order ordinary differential equation

Existence of weak solutions for a boundary value problem of a second order ordinary differential equation

Existence of mild solutions to semilinear fractional evolution equation using Krasnoselskii fixed point theorem

Numerical Analysis of the Chebyshev Collocation Method for Functional Volterra Integral Equations

Contact Info

Product

Resources

About