in this paper, a numerical solution for a system of linear fredholm integro-differential equations by means of the sinc method is considered. this approximation reduces the system of integro-differential equations to an explicit system of algebraic equations. the exponential convergence rate $o(e^{-k sqrt{n}})$ of the method is proved. the analytical results are illustrated with numerical examp...

In this paper, a numerical solution for a system of linear Fredholm integro-differential equations by means of the sinc method is considered. This approximation reduces the system of integro-differential equations to an explicit system of algebraic equations. The exponential convergence rate $O(e^{-k sqrt{N}})$ of the method is proved. The analytical results are illustrated with numerical examp...

The paper studies the finite-time blow-up theory for a class of nonlinear Volterra integro-differential equations. The conditions for the occurrence of finite-time blow-up for nonlinear Volterra integro-differential equations are provided. Moreover, the finite-time blow-up theory for nonlinear partial Volterra integro-differential equations with general kernels is also established using the blo...

This paper presents a numerical matrix method based on Bernstein polynomials (BPs) for approximate the solution of a system of m-th order nonlinear Volterra integro-differential equations under initial conditions. The approach is based on operational matrices of BPs. Using the collocation points,this approach reduces the systems of Volterra integro-differential equations associated with the giv...

In this paper, the variational iteration method for solving nth-order fuzzy integro differential equations (nth-FIDE) is proposed. In fact the problem is changed to the system of ordinary fuzzy integro-differential equations and then fuzzy solution of nth-FIDE is obtained. Some examples show the efficiency of the proposed method.

This paper is concerned with the existence of mild solutions for impulsive integro-differential equations with nonlocal conditions. We apply the technique measure of noncompactness in the space of piecewise continuous functions and by using Darbo-Sadovskii's fixed point theorem, we prove reasults about impulsive integro-differential equations for convex-power condensing operators.

in this letter, the numerical scheme of nonlinear volterra-fredholm integro-differential equations is proposed in a reproducing kernel hilbert space (rkhs). the method is constructed based on the reproducing kernel properties in which the initial condition of the problem is satised. the nonlinear terms are replaced by its taylor series. in this technique, the nonlinear volterra-fredholm integr...

Recently, there has been significant development in the existence of mild solutions for fractional semilinear integro-differential equations but optimal control is not provided. The aim of this paper is studying optimal feedback control for fractional semilinear integro-differential equations in an arbitrary Banach space associated with operators ...

Asymptotic equilibria of linear integro-differential equations and asymptotic relations between solutions of linear homogeneous impulsive differential equations and those of linear integro-differential equations are established. A new Gronwall–Bellman type lemma for integro-differential inequalities is proved. An example is given to demonstrate the validity of one of the results. c © 2008 Elsev...