scholarly journals Fuzzy Integral Equations and Strong Fuzzy Henstock Integrals

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Yabin Shao ◽  
Huanhuan Zhang
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Convergence Theorem ◽  
Existence Theorems ◽  
Fuzzy Integral ◽  
Henstock Integral

By using the strong fuzzy Henstock integral and its controlled convergence theorem, we generalized the existence theorems of solution for initial problems of fuzzy discontinuous integral equation.

scholarly journals Deferred correction for the integral equation eigenvalue problem

1981 ◽  
Vol 22 (4) ◽  
pp. 474-487 ◽  
Author(s):  
K. W. Chu ◽  
A. Spence
Keyword(s):  
Integral Equation ◽  
Eigenvalue Problem ◽  
Integral Equations ◽  
Convergence Theorem ◽  
Eigenvalues And Eigenfunctions ◽  
Deferred Correction ◽  
Numerical Example

AbstractThis paper considers the improvement of approximate eigenvalues and eigenfunctions of integral equations using the method of deferred correction. A convergence theorem is proved and a numerical example illustrating the theory is given.

scholarly journals Quadrature Rules and Iterative Method for Numerical Solution of Two-Dimensional Fuzzy Integral Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-18 ◽  
Author(s):  
S. M. Sadatrasoul ◽  
R. Ezzati
Keyword(s):  
Integral Equations ◽  
Iterative Procedure ◽  
Numerical Experiments ◽  
Quadrature Rules ◽  
Fredholm Integral Equations ◽  
Fuzzy Integral ◽  
Two Dimensional ◽  
Henstock Integral ◽  
Uniform Modulus Of Continuity ◽  
Theoretical Results

We introduce some generalized quadrature rules to approximate two-dimensional, Henstock integral of fuzzy-number-valued functions. We also give error bounds for mappings of bounded variation in terms of uniform modulus of continuity. Moreover, we propose an iterative procedure based on quadrature formula to solve two-dimensional linear fuzzy Fredholm integral equations of the second kind (2DFFLIE2), and we present the error estimation of the proposed method. Finally, some numerical experiments confirm the theoretical results and illustrate the accuracy of the method.

scholarly journals On existence theorems for some generalized nonlinear functional-integral equations with applications

Filomat ◽  
2017 ◽  
Vol 31 (7) ◽  
pp. 2081-2091 ◽  
Author(s):  
Mishra Narayan ◽  
Mausumi Sen ◽  
Ram Mohapatra
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Banach Algebra ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Existence Theorems ◽  
Functional Integral ◽  
Measures Of Noncompactness ◽  
Nonlinear Functional ◽  
Functional Integral Equations

In the present paper, utilizing the techniques of suitable measures of noncompactness in Banach algebra, we prove an existence theorem for nonlinear functional-integral equation which contains as particular cases several integral and functional-integral equations that appear in many branches of nonlinear analysis and its applications. We employ the fixed point theorems such as Darbo?s theorem in Banach algebra concerning the estimate on the solutions. We also provide a nontrivial example that explains the generalizations and applications of our main result.

scholarly journals Homotopy Analysis Method to Solve Two-Dimensional Nonlinear Volterra-Fredholm Fuzzy Integral Equations

2020 ◽  
Vol 4 (1) ◽  
pp. 9
Author(s):  
Atanaska Georgieva ◽  
Snezhana Hristova
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Homotopy Analysis Method ◽  
Approximate Solutions ◽  
Fredholm Integral Equations ◽  
Fuzzy Integral ◽  
Two Dimensional ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Fuzzy Solution

The main goal of the paper is to present an approximate method for solving of a two-dimensional nonlinear Volterra-Fredholm fuzzy integral equation (2D-NVFFIE). It is applied the homotopy analysis method (HAM). The studied equation is converted to a nonlinear system of Volterra-Fredholm integral equations in a crisp case. Approximate solutions of this system are obtained by the help with HAM and hence an approximation for the fuzzy solution of the nonlinear Volterra-Fredholm fuzzy integral equation is presented. The convergence of the proposed method is proved and the error estimate between the exact and the approximate solution is obtained. The validity and applicability of the proposed method is illustrated on a numerical example.

scholarly journals The Strong Fuzzy Henstock Integrals and Discontinuous Fuzzy Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Yabin Shao ◽  
Huanhuan Zhang
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Convergence Theorem ◽  
Continuous Dependence ◽  
Existence Theorems ◽  
Henstock Integral

We generalized the existence theorems and the continuous dependence of a solution on parameters for initial problems of fuzzy discontinuous differential equation by the strong fuzzy Henstock integral and its controlled convergence theorem.

scholarly journals Solving the First Kind Fuzzy Integral Equations Using a Hybrid Regularization Method and Bernstein Polynomials

2016 ◽  
Vol 10 (9) ◽  
pp. 22 ◽  
Author(s):  
A. K. Moloodpour ◽  
A. Jafarian
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Regularization Method ◽  
Bernstein Polynomials ◽  
The Other ◽  
Fuzzy Integral

A hybrid of regularization methodand Bernstein polynomials is used to solve the first kind fuzzy integral equations. In this paper, first the regularization method applied to convert the first kind fuzzy integral equation into the second kind fuzzy integral equation. Then by approximating Bernstein polynomials, the obtained second kind fuzzy integral equation is solved. In this method, one parameter was created in the second kind equation. When this parameter tends to zero, the solutions of integral equation of the second kind tend to solutions of the integral equation of the first kind. The obtained solutions are comparable to the solutions of the other similar methods. Performance of the mentioned method is illustrated by considering some example.

scholarly journals Bounded solutions for fuzzy integral equations

2002 ◽  
Vol 31 (2) ◽  
pp. 109-114 ◽  
Author(s):  
D. N. Georgiou ◽  
I. E. Kougias
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Fuzzy Integral ◽  
Bounded Solutions

We study conditions under which the solutions of a fuzzy integral equation are bounded.

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