The paper presents the semi-numerical solution for the magnetohydrodynamic (MHD) viscous flow due to a stretching sheet caused by boundary layer of an incompressible viscous flow. The governing partial differential equations of momentum equations are reduced into a nonlinear ordinary differential equation (NODE) by using a classical similarity transformation along with appropriate boundary cond...

in this paper, first the properties of one and two-dimensional differential transforms are presented.next, by using the idea of differential transform, we will present a method to find an approximate solution fora volterra integro-partial differential equations. this method can be easily applied to many linear andnonlinear problems and is capable of reducing computational works. in some particu...

In this paper, we study algorithmic aspects of linear ordinary integro-differential operators with polynomial coefficients. Even though this algebra is not noetherian and has zero divisors, Bavula recently proved that it is coherent, which allows one to develop an algebraic systems theory. For an algorithmic approach to linear systems theory of integro-differential equations with boundary condi...

The aim of this paper is to establish the existence of solutions of boundary value problems of nonlinear fractional integro-differential equations involving Caputo fractional derivative by using the techniques such as fractional calculus, H"{o}lder inequality, Krasnoselskii's fixed point theorem and nonlinear alternative of Leray-Schauder type. Examples are exhibited to illustrate the main resu...

the spline collocation method  is employed to solve a system of linear and nonlinear fredholm and volterra integro-differential equations. the solutions are collocated by cubic b-spline and the integrand is approximated by the newton-cotes formula. we obtain the unique solution for linear and nonlinear system $(nn+3n)times(nn+3n)$ of integro-differential equations. this approximation reduces th...

In this article, we use two concepts, measure of non-compactness and Meir-Keeler condensing operators. The measure of non-compactness has been applied for existence of solution nonlinear integral equations, ordinary differential equations and system of differential equations in the case of finite and infinite dimensions by some authors. Also Meir-Keeler condensing operators are shown in some pa...

In this paper, we present some results on the existence of periodic solutions to Volterra integro-differential equations of neutral type. The main idea is to show the convergence of an equibounded sequence of periodic solutions of certain limiting equations which are of finite delay. This makes it possible to apply the existing Liapunov-Razumikhin technique for neutral equations with finite del...

In this paper, the variational iteration method proposed by Ji-Huan He is applied to solve both linear and nonlinear boundary value problems for fourth order integro-differential equations. The numerical results obtained with minimum amount of computation are compared with the exact solutions to show the efficiency of the method. The results show that the variational iteration method is of high...

This paper regards initial value problem for second order impulsive integro-differential equations as some nonlinear vector system. By means of the Mönch′s fixed point theorem, some existence theorems of solutions of the initial value problem are established. The results are newer than all of the previous ones because of the more general form compactness-type condition and the weaker restrictio...