in this work, we conduct a comparative study among the combine laplace transform and modied adomian decomposition method (lmadm) and two traditional methods for an analytic and approximate treatment of special type of nonlinear volterra integro-differential equations of the second kind. the nonlinear part of integro-differential is approximated by adomian polynomials, and the equation is red...

A class of singular integro-differential equations in Lebesgue spaces are studied. There are many applications of the singular integro-differential equations discussed in this paper. An example in modeling the stress distribution of an elastic medium with holes is discussed in the paper. Direct numerical schemes using a collocation method and a mechanical quadrature rule designed for the singul...

In this paper, we investigate the existence result for nonlinear impulsive fractional integro-differential equations with boundary conditions by using fixed point theorem and Green's function. I. INTRODUCTION The topic of fractional differential equations has received a great deal of attention from many scientists and researchers during the past decades; see [1-7]. This is mostly due to the fac...

In this note we prove the stochastic homogenization for a large class of fully nonlinear elliptic integro-differential equations in stationary ergodic random environments. Such equations include, but are not limited to Bellman equations and the Isaacs equations for the control and differential games of some pure jump processes in a random, rapidly varying environment. The translation invariant ...

In this paper we consider the nonlinear parabolic integro-differential equation with initial and boundary conditions. We develop the method of generalized quasilinearization to generate linear iterates that converge quadratically to the unique solution of the nonlinear parabolic integro-differential equation. For this purpose, we establish comparison results for the parabolic integro-differenti...

The present paper deals with the numerical solution for a general form of system nonlinear Volterra delay integro-differential equations (VDIDEs). main purpose this work is to provide a...

in this paper, we study the numerical solution of hybrid fuzzy differential equations by using differential transformation method (dtm). this is powerful method which consider the approximate solution of a nonlinear equation as an infinite series usually converging to the accurate solution. several numerical examples are given and by comparing the numerical results obtained from dtm  and  predi...

We present a theory to describe the transient and steady state behaviors of the active modes of a photonic crystal with active constituents (active photonic crystal). Using a couple mode model, we showed that the full vectorial Maxwell-Bloch equations describing the physics of light matter interaction in the active photonic crystal can be written as a system of integro-differential equations. U...

We consider the mode coupling theory (MCT) of glass transition for a binary fluid. The equations of nonlinear fluctuating hydrodynamics for the compressible fluid are obtained with a proper choice of slow variables which correspond to the conservation laws in the system. The resulting model equations are used to obtain a coupled set of nonlinear integro-differential equations for the various co...