• 호남수학학술지
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• 제26권4호
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• pp.455-462
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• 2004

We prove that if ${\mathbb{K}}^*$ is adjoint operator on $W_2{^2}({\Omega})$, then ${\mathbb{K}}^*v(t,\;{\tau})=,\;v(x,\;y){\in}W_2{^2}({\Omega})$ ; it is also related to the decomposition of solution of Fredholm equations.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제21권1호
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• pp.17-28
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• 2017

A combined form of the modified Laplace Adomian decomposition method (LADM) is developed for the analytic treatment of the nonlinear Volterra-Fredholm integro differential equations. This method is effectively used to handle nonlinear integro differential equations of the first and the second kind. Finally, some examples will be examined to support the proposed analysis.

• Journal of applied mathematics & informatics
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• 제19권1_2호
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• pp.415-425
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• 2005

This paper outlines a reliable strategy for solving nonlinear Volterra-Fredholm integro-differential equations. The modified form of Adomian decomposition method is found to be fast and accurate. Numerical examples are presented to illustrate the accuracy of the method.

• Journal of applied mathematics & informatics
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• 제7권3호
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• pp.801-812
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• 2000

Two-dimensional slow viscous flow on infinite half-plane past a perpendicular infinite cavity is considered on the basis of the Stokes approximation. Using complex representation of the two-dimensional Stokes flow, the problem is reduced to solving a set of Fredholm integral equations of the second kind. The streamlines and the pressure and vorticity distribution on the wall are numerically determined.

• 대한수학회지
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• 제45권1호
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• pp.121-136
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• 2008

Some new explicit bounds on the solutions to a class of new nonlinear retarded Volterra-Fredholm type integral inequalities in two independent variables are established, which can be used as effective tools in the study of certain integral equations. Some examples of application are also indicated.

• Journal of applied mathematics & informatics
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• 제12권1_2호
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• pp.165-182
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• 2003

Toeplitz matrix method and the product Nystrom method are described for mixed Fredholm-Volterra singular integral equation of the second kind with Carleman Kernel and logarithmic kernel. The results are compared with the exact solution of the integral equation. The error of each method is calculated.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제17권1호
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• pp.17-28
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• 2013

In this paper, we study the global existence of solutions for the initial value problems for Volterra-Fredholm type functional impulsive integrodifferential equations. Using the Leray-Schauder Alternative, we derive conditions under which a solution exists globally.

• Journal of applied mathematics & informatics
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• 제9권1호
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• pp.261-275
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• 2002

Besides asymptotic method, the method of orthogonal polynomials has been used to obtain the solution of the Fredholm integral equation. The principal (singular) part of the kerne1 which corresponds to the selected domain of parameter variation is isolated. The unknown and known functions are expanded in a Chebyshev polynomial and an infinite a1gebraic system is obtained.

• 충청수학회지
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• 제32권4호
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• pp.409-420
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• 2019

In this article, we discussed semi-analytical approximated methods for solving mixed Volterra-Fredholm integro-differential equations, namely: Adomian decomposition method and modified Adomian decomposition method. Moreover, we prove the uniqueness results and convergence of the techniques. Finally, an example is included to demonstrate the validity and applicability of the proposed techniques.

• Nonlinear Functional Analysis and Applications
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• 제28권1호
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• pp.237-249
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• 2023

In this paper, by means of the Schauder fixed point theorem and Arzela-Ascoli theorem, the existence and uniqueness of solutions for a class of not instantaneous impulsive problems of nonlinear fractional functional Volterra-Fredholm integro-differential equations are investigated. An example is given to illustrate the main results.