• The Pure and Applied Mathematics
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• v.24 no.1
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• pp.1-19
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• 2017

In this paper we obtain some integral inequalities by using Stieltjes derivatives, and we apply our results to the study of asymptotic behavior of a certain second-order integro-differential equation.

• The Pure and Applied Mathematics
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• v.24 no.3
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• pp.155-169
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• 2017

In this paper we obtain some integral inequalities involving impulses and apply our results to a certain integro-differential equation with impulses. First, we obtain a bound of the equation, and we use the bound to study some qualitative properties of the equation.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.4
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• pp.511-517
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• 2008

In this paper, we investigate h-stability of nonlinear integro-differential equations.

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.981-992
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• 2012

Integro-differential equations arise in modeling various physical and engineering problems. Several numerical and analytical methods have been developed to solving such equations. We introduce the NHPM for solving nonlinear integro-differential equations. Several examples for solving integro-differential equations are presented to illustrate the efficiency of the proposed NHPM.

• Journal of applied mathematics & informatics
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• v.31 no.3_4
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• pp.499-511
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• 2013

In this article, Adomian decomposition method (ADM), variation iteration method(VIM) and homotopy analysis method (HAM) for solving integro-differential equation with singular kernel have been investigated. Also,we study the existence and uniqueness of solutions and the convergence of present methods. The accuracy of the proposed method are illustrated with solving some numerical examples.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.20 no.3
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• pp.261-275
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• 2016

In this paper, an integro-differential equation which arises in oscillating magnetic fields is studied. The generalized fractional order Chebyshev orthogonal functions (GFCF) collocation method used for solving this integral equation. The GFCF collocation method can be used in applied physics, applied mathematics, and engineering applications. The results of applying this procedure to the integro-differential equation with time-periodic coefficients show the high accuracy, simplicity, and efficiency of this method. The present method is converging and the error decreases with increasing collocation points.

• Journal of the Chungcheong Mathematical Society
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• v.13 no.1
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• pp.45-51
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• 2000

We will investigate some properties of integro-delay-differential equations, $$x^{\prime}(t)=A(t)x(t-g_1(t,x_t))+{\int}_{t_0}^{t}B(t,s)x(s-g_2(s,x_s))ds,\;t_0{\geq}0,\\x(t_0)={\phi}$$,

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.21 no.1
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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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• v.33 no.5_6
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• pp.699-721
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• 2015

This paper investigates the existence of mild solution for a fractional integro-differential equations with a deviating argument and nonlocal initial condition in an arbitrary separable Hilbert space H via technique of approximations. We obtain an associated integral equation and then consider a sequence of approximate integral equations obtained by the projection of considered associated nonlocal fractional integral equation onto finite dimensional space. The existence and uniqueness of solutions to each approximate integral equation is obtained by virtue of the analytic semigroup theory via Banach fixed point theorem. Next we demonstrate the convergence of the solutions of the approximate integral equations to the solution of the associated integral equation. We consider the Faedo-Galerkin approximation of the solution and demonstrate some convergenceresults. An example is also given to illustrate the abstract theory.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2004.10a
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• pp.345-350
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• 2004

In this paper we study the controllability for the nonlinear fuzzy integro-differential equations on E$_{N}$$^{n}$ by using the concept of fuzzy number of dimension n whose values are normal, convex, upper semicontinuous and compactly supported surface in R$^n$. E$_{N}$$^{n}$ be the set of all fuzzy numbers in R$^n$ with edges having bases parallel to axis X$_1$, X$_2$, …, X$_{n}$ .X> .