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.

In this paper, an effective numerical method is introduced for the treatment of nonlinear two-dimensional Volterra-Fredholm integro-differential equations. Here, we use the so-called two-dimensional block-pulse functions.First, the two-dimensional block-pulse operational matrix of integration and differentiation has been presented. Then, by using this matrices, the nonlinear two-dimensional Vol...

‎semidiscrete finite element approximation of a hyperbolic type‎ ‎integro-differential equation is studied. the model problem is‎ ‎treated as the wave equation which is perturbed with a memory term.‎ ‎stability estimates are obtained for a slightly more general problem.‎ ‎these, based on energy method, are used to prove optimal order‎ ‎a priori error estimates.‎

In this study, a sufficient condition for the existence and uniqueness of some fractional order Integral-Differential equations is obtained. Therefore, fixed point method used to solve differential equation problem involving nonlinear degree integrals. addition, results found supported by examples.

In this paper we discuss the numerical solution of initial-boundary value problem for the fourth order parabolic partial integro-differential equation. We use the forward Euler scheme for time discretization and the quasi-wavelet method for space discretization. Sometimes, we give a new method about the treatment of boundary condition. Numerical experiment is included to demonstrate the validit...

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.

Sufficient conditions are given under which the nonlinear n-th order differential equation with quasiderivatives has oscillatory solutions. AMS Subject Classification. 34C10