scholarly journals Uniqueness of the Hadamard-type integral equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Chenkuan Li
Keyword(s):  
Banach Spaces ◽  
Integral Equations ◽  
Coupled System ◽  
Contraction Principle ◽  
Uniqueness Of Solutions ◽  
Type Integral ◽  
Banach’S Contraction Principle

AbstractThe goal of this paper is to study the uniqueness of solutions of several Hadamard-type integral equations and a related coupled system in Banach spaces. The results obtained are new and based on Babenko’s approach and Banach’s contraction principle. We also present several examples for illustration of the main theorems.

scholarly journals Uniqueness of Solutions of the Generalized Abel Integral Equations in Banach Spaces

2021 ◽  
Vol 5 (3) ◽  
pp. 105
Author(s):  
Chenkuan Li ◽  
Hari M. Srivastava
Keyword(s):  
Banach Spaces ◽  
Integral Equations ◽  
Coupled System ◽  
Contraction Principle ◽  
Uniqueness Of Solutions ◽  
Abel Integral Equations ◽  
Banach’S Contraction Principle

This paper studies the uniqueness of solutions for several generalized Abel’s integral equations and a related coupled system in Banach spaces. The results derived are new and based on Babenko’s approach, Banach’s contraction principle and the multivariate Mittag–Leffler function. We also present some examples for the illustration of our main theorems.

scholarly journals New Explicit Bounds on Gamidov Type Integral Inequalities for Functions in Two Variables and Their Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Kelong Cheng ◽  
Chunxiang Guo
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Integral Inequalities ◽  
Fredholm Integral Equations ◽  
Uniqueness Of Solutions ◽  
Fredholm Type ◽  
Type Integral ◽  
Explicit Bounds ◽  
Linear And Nonlinear

Some linear and nonlinear Gamidov type integral inequalities in two variables are established, which can give the explicit bounds on the solutions to a class of Volterra-Fredholm integral equations. Some examples of application are presented to show boundedness and uniqueness of solutions of a Volterra-Fredholm type integral equation.

Global solutions for Volterra ordinary and retarded integral equations

2008 ◽  
Vol 41 (3) ◽  
Author(s):  
Bianca Satco
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Integral Equations ◽  
Point Theorem ◽  
Global Solutions ◽  
Volterra Type ◽  
Darbo’S Fixed Point Theorem ◽  
Type Integral

AbstractUsing a generalization of Darbo’s fixed point theorem, we obtain the existence of global solutions for nonlinear Volterra-type integral equations in Banach spaces. The involved functions are supposed to be continuous only with respect to some variables, integrability or essential boundedness conditions being also imposed. Our result improves the similar result given in [

scholarly journals The Solutions of Mixed Monotone Fredholm-Type Integral Equations in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Hua Su
Keyword(s):  
Boundary Value Problem ◽  
Banach Spaces ◽  
Unique Solution ◽  
Integral Equations ◽  
Nonlinear Ordinary Differential Equations ◽  
Point Boundary ◽  
Fredholm Type ◽  
Monotone Iterative ◽  
Type Integral ◽  
Ordered Banach Spaces

By introducing new definitions ofϕconvex and-φconcave quasioperator andv0quasilower andu0quasiupper, by means of the monotone iterative techniques without any compactness conditions, we obtain the iterative unique solution of nonlinear mixed monotone Fredholm-type integral equations in Banach spaces. Our results are even new toϕconvex and-φconcave quasi operator, and then we apply these results to the two-point boundary value problem of second-order nonlinear ordinary differential equations in the ordered Banach spaces.

scholarly journals New Lyapunov-type inequalities for fractional multi-point boundary value problems involving Hilfer-Katugampola fractional derivative

2021 ◽  
Vol 7 (1) ◽  
pp. 1074-1094
Author(s):  
Wei Zhang ◽  
◽  
Jifeng Zhang ◽  
Jinbo Ni
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Boundary Value Problems ◽  
Integral Equations ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Contraction Principle ◽  
Point Boundary ◽  
Fractional Differential ◽  
Banach’S Contraction Principle

<abstract><p>In this paper, we present new Lyapunov-type inequalities for Hilfer-Katugampola fractional differential equations. We first give some unique properties of the Hilfer-Katugampola fractional derivative, and then by using these new properties we convert the multi-point boundary value problems of Hilfer-Katugampola fractional differential equations into the equivalent integral equations with corresponding Green's functions, respectively. Finally, we make use of the Banach's contraction principle to derive the desired results, and give a series of corollaries to show that the current results extend and enrich the previous results in the literature.</p></abstract>

scholarly journals Solvability of Coupled Systems of Generalized Hammerstein-Type Integral Equations in the Real Line

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 111 ◽  
Author(s):  
Feliz Minhós ◽  
Robert de Sousa
Keyword(s):  
Integral Equations ◽  
Real Line ◽  
Coupled System ◽  
Continuous Functions ◽  
Kernel Functions ◽  
Coupled Systems ◽  
Type Integral ◽  
First Time ◽  
Derivatives Of ◽  
Different Order

In this work, we consider a generalized coupled system of integral equations of Hammerstein-type with, eventually, discontinuous nonlinearities. The main existence tool is Schauder’s fixed point theorem in the space of bounded and continuous functions with bounded and continuous derivatives on R , combined with the equiconvergence at ± ∞ to recover the compactness of the correspondent operators. To the best of our knowledge, it is the first time where coupled Hammerstein-type integral equations in real line are considered with nonlinearities depending on several derivatives of both variables and, moreover, the derivatives can be of different order on each variable and each equation. On the other hand, we emphasize that the kernel functions can change sign and their derivatives in order to the first variable may be discontinuous. The last section contains an application to a model to study the deflection of a coupled system of infinite beams.

scholarly journals Existence of solutions of Oseen type integral equations

1984 ◽  
Vol 29 (1) ◽  
pp. 57-66
Author(s):  
J.A. Belward
Keyword(s):  
Integral Equations ◽  
Existence Of Solutions ◽  
Logarithmic Singularity ◽  
Boundary Value ◽  
Uniqueness Of Solutions ◽  
Fredholm Equations ◽  
Exterior Boundary ◽  
Flow And Heat Transfer ◽  
Type Integral ◽  
Exterior Boundary Value Problem

Integral equations of Oseen type are first kind Fredholm equations whose kernels have a logarithmic singularity. They arise in exterior boundary value problems in fluid flow and heat transfer. Subject to the assumption of uniqueness of solutions of the parent exterior boundary value problem, solutions of the Oseen type integral equations are shown to exist.

A fully Hadamard type integral boundary value problem of a coupled system of fractional differential equations

2014 ◽  
Vol 17 (2) ◽  
Author(s):  
Bashir Ahmad ◽  
Sotiris Ntouyas
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Integral Boundary Conditions ◽  
Coupled System ◽  
Uniqueness Of Solutions ◽  
Integral Boundary ◽  
Type Integral ◽  
Fractional Differential

AbstractThis paper is concerned with the existence and uniqueness of solutions for a coupled system of Hadamard type fractional differential equations and integral boundary conditions. We emphasize that much work on fractional boundary value problems involves either Riemann-Liouville or Caputo type fractional differential equations. In the present work, we have considered a new problem which deals with a system of Hadamard differential equations and Hadamard type integral boundary conditions. The existence of solutions is derived from Leray-Schauder’s alternative, whereas the uniqueness of solution is established by Banach’s contraction principle. An illustrative example is also included.

scholarly journals On the nonlinear Hadamard-type integro-differential equation

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Chenkuan Li
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Continuous Functions ◽  
Contraction Principle ◽  
Uniqueness Of Solutions ◽  
Absolutely Continuous Functions ◽  
Absolutely Continuous ◽  
Integro Differential Equation ◽  
Banach’S Contraction Principle

AbstractThis paper studies uniqueness of solutions for a nonlinear Hadamard-type integro-differential equation in the Banach space of absolutely continuous functions based on Babenko’s approach and Banach’s contraction principle. We also include two illustrative examples to demonstrate the use of main theorems.

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