In the course of this paper, the Optimal Homotopy Asymptotic Method (OHAM) introduced by Marica is applied to solve linear and nonlinear boundary value problems both for fourth-order integro-differential equations. The following analysis is accompanied by numerical examples whose results show that the Optimal Homotopy Asymptotic Method is highly accurate, convenient and relatively efficient for...

In this paper will be compared between Adomian decomposition method (ADM) and Taylor expansion method (TEM) for solving (approximately) a class of fractional integro-differential equations. Numerical examples are presented to illustrate the efficiency and accuracy of the proposed methods. General Terms Numerical solutions, Fractional integro-differential equations.

In this paper, a modification of variational iteration method is applied to solve fractional integro-differential equations. The fractional derivative is considered in the Caputo sense. Through examples, we will see the modified method performs extremely effective in terms of efficiency and simplicity to solve fractional integro-differential equations. 2000 Mathematics Subject Classification: 6...

The Laplace decomposition method (LDM) has been implemented on integro-differential equations to calculate the analytical exact solutions. Obtained results show the effectiveness, reliability and convergence of the proposed method. It may be concluded that the proposed method is a powerful tool for solving the integro-differential equations and other wide class of mathematical problems.

In this paper, we deal with a class of backward stochastic differential equations driven by Teugels martingales associated with a Lévy process (BSDELs). The comparison theorem is obtained. It is also shown that the solution of BSDE provides a viscosity solution of the associated system with partial integro-differential equations.

In this paper we study the existence of classical solutions for a class of abstract neutral integro-differential equation with unbounded delay. A concrete application to partial neutral integro-differential equations is considered.

Some new stability results are given for a delay integro-differential equation. A basis theorem on the behavior of solutions of delay integro-differential equations is established. As a consequence of this theorem, a stability criterion is obtained.

A new and effective direct method to determine the numerical solution of specific nonlinear Volterra-Fredholm integral and integro-differential equations is proposed. The method is based on vector forms of block-pulse functions (BPFs). By using BPFs and its operational matrix of integration, an integral or integro-differential equation can be transformed to a nonlinear system of algebraic equat...