scholarly journals Data dependence of solutions for Fredholm-Volterra integral equations in L2[a, b]

2013 ◽  
Vol 5 (1) ◽  
pp. 5-19
Author(s):  
Szilárd András
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Continuous Dependence ◽  
Main Tool ◽  
Volterra Integral Equations ◽  
Data Dependence ◽  
Solution Operator ◽  
Volterra Type ◽  
Type Integral

Abstract In this paper we study the continuous dependence and the differentiability with respect to the parameter λ ∈ [λ1, λ2] of the solution operator S : [λ1, λ2] → L2[a, b] for a mixed Fredholm-Volterra type integral equation. The main tool is the fiber Picard operators theorem (see [9], [8], [11], [3] and [2]).

A Novel Analytical Implementation of Nonlinear Volterra Integral Equations

2012 ◽  
Vol 67 (12) ◽  
pp. 674-678 ◽  
Author(s):  
Majid Khan ◽  
Muhammad Asif Gondal ◽  
Syeda Iram Batool
Keyword(s):  
Exact Solutions ◽  
Integral Equations ◽  
Volterra Integral Equations ◽  
Volterra Equations ◽  
Volterra Type ◽  
Transform Method ◽  
Novel Technique ◽  
Homotopy Perturbation ◽  
Type Integral ◽  
Nonlinear Volterra Equations

This article aims at preferring a new and viable algorithm, specifically a two-step homotopy perturbation transform algorithm (TSHPTA). This novel technique is a feasible way in finding exact solutions with a small amount of calculations. As a simple but typical example, it demonstrates the strength and the great potential of the two-step homotopy perturbation transform method to solve nonlinear Volterra-type integral equations efficiently. The results reveal that the proposed scheme is suitable for the nonlinear Volterra equations.

QUANTUM INTEGRAL EQUATIONS OF VOLTERRA TYPE WITH GENERALIZED OPERATOR-VALUED KERNELS

2000 ◽  
Vol 03 (04) ◽  
pp. 505-517 ◽  
Author(s):  
ZHIYUAN HUANG ◽  
CAISHI WANG ◽  
XIANGJUN WANG
Keyword(s):  
Integral Equation ◽  
Explicit Expression ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Continuous Dependence ◽  
Uniqueness Of Solutions ◽  
Volterra Type ◽  
Quantum Integral ◽  
Generalized Operator

Quantum integral equation of Volterra type with generalized operator-valued kernel is introduced. Existence and uniqueness of solutions are established, explicit expression of the solution is given, the continuity, continuous dependence on free terms and other properties of the solution are proved.

scholarly journals A nonstandard Volterra integral equation on time scales

2019 ◽  
Vol 52 (1) ◽  
pp. 503-510 ◽  
Author(s):  
Andrejs Reinfelds ◽  
Shraddha Christian
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Time Scales ◽  
Continuous Dependence ◽  
Sufficient Conditions ◽  
Functional Space ◽  
Volterra Type ◽  
Type Integral ◽  
Banach’S Fixed Point Theorem ◽  
Continuous Dependence Of Solutions

AbstractThis paper introduces the more general result on existence, uniqueness and boundedness for solutions of nonstandard Volterra type integral equation on an arbitrary time scales. We use Lipschitz type function and the Banach’s fixed point theorem at functional space endowed with a suitable Bielecki type norm. Furthermore, it allows to get new sufficient conditions for boundedness and continuous dependence of solutions.

EXISTENCE OF SOLUTION FOR A VOLTERRA TYPE INTEGRAL EQUATION USING DARBO-TYPE F-CONTRACTION

2021 ◽  
Vol 10 (6) ◽  
pp. 2687-2710
Author(s):  
F. Akutsah ◽  
A. A. Mebawondu ◽  
O. K. Narain
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Existence Of Solution ◽  
Volterra Type ◽  
Complete Metric Spaces ◽  
Type Integral ◽  
New Type

In this paper, we provide some generalizations of the Darbo's fixed point theorem and further develop the notion of $F$-contraction introduced by Wardowski in (\cite{wad}, D. Wardowski, \emph{Fixed points of a new type of contractive mappings in complete metric spaces,} Fixed Point Theory and Appl., 94, (2012)). To achieve this, we introduce the notion of Darbo-type $F$-contraction, cyclic $(\alpha,\beta)$-admissible operator and we also establish some fixed point and common fixed point results for this class of mappings in the framework of Banach spaces. In addition, we apply our fixed point results to establish the existence of solution to a Volterra type integral equation.

scholarly journals Extended partial b-metric spaces and some fixed point results

Filomat ◽  
2018 ◽  
Vol 32 (8) ◽  
pp. 2837-2850 ◽  
Author(s):  
V. Parvaneh ◽  
Z. Kadelburg
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Metric Spaces ◽  
Volterra Type ◽  
Fundamental Lemma ◽  
Contractive Mappings ◽  
Type Integral ◽  
Convergence Of Sequences ◽  
Weakly Contractive

In this paper, we introduce the concept of extended partial b-metric space. We demonstrate a fundamental lemma for the convergence of sequences in such spaces. Then we prove some fixed point results for weakly contractive mappings in the setup of ordered extended partial b-metric spaces. An example is given to verify the effectiveness and applicability of our main results. An application of these results to Volterra-type integral equations is provided at the end.

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.

scholarly journals Resolvent, Natural, and Sumudu Transformations: Solution of Logarithmic Kernel Integral Equations with Natural Transform

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Kevser Köklü
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Volterra Integral Equations ◽  
Logarithmic Kernel ◽  
Sumudu Transform

In this paper, the resolvent of an integral equation was found with natural transform which is a new transformation which converged to Laplace and Sumudu transformations, and the result was confirmed by the Sumudu transform. At the same time, a solution to the first type of logarithmic kernel Volterra integral equations has been produced by the natural transform.

A volterra-type integral equation

1989 ◽  
Vol 40 (4) ◽  
pp. 438-442 ◽  
Author(s):  
S. Ashirov ◽  
Ya. D. Mamedov
Keyword(s):  
Integral Equation ◽  
Volterra Type ◽  
Type Integral

scholarly journals On the Solutions of a Class of Integral Equations Pertaining to Incomplete H-Function and Incomplete H-Function

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 819
Author(s):  
Manish Kumar Bansal ◽  
Devendra Kumar ◽  
Jagdev Singh ◽  
Kottakkaran Sooppy Nisar
Keyword(s):  
Integral Equation ◽  
Fractional Calculus ◽  
Integral Equations ◽  
Real World ◽  
Mellin Transform ◽  
Fredholm Type ◽  
Type Integral ◽  
Real World Problems

The main aim of this article is to study the Fredholm-type integral equation involving the incomplete H-function (IHF) and incomplete H-function in the kernel. Firstly, we solve an integral equation associated with the IHF with the aid of the theory of fractional calculus and Mellin transform. Next, we examine an integral equation pertaining to the incomplete H-function with the help of theory of fractional calculus and Mellin transform. Further, we indicate some known results by specializing the parameters of IHF and incomplete H-function. The results computed in this article are very general in nature and capable of giving many new and known results connected with integral equations and their solutions hitherto scattered in the literature. The derived results are very useful in solving various real world problems.

Sign in / Sign up

Export Citation Format

Share Document