One of the classical topics in the qualitative theory of differential equations is the Floquet theory. It provides a means to represent solutions and helps in particular for stability analysis. In this paper first we shall study Floquet theory for integro-differential equations (IDE), and then employ it to address stability problems for linear and nonlinear equations.

In this paper the one-dimensional two-phase Stefan problem is studied analytically leading to a system of non-linear Volterra-integral-equations describing heat distribution in each phase. For unified transform method has been employed which provides via global relation, by these problems can be solved using integral representations. To do this, underlying partial differential equation rewritte...

We prove a regularity result for solutions of a purely integro-differential Bellman equation. This regularity is enough for the solutions to be understood in the classical sense. If we let the order of the equation approach two, we recover the theorem of Evans and Krylov about the regularity of solutions to concave uniformly elliptic partial differential equations.

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...

s of PhD Theses at Irish Universities 2007 On the Asymptotic Behaviour of Deterministic and Stochastic Volterra Integro–Differential Equations

We discuss the approximate controllability of nonlinear fractional integro-differential system under the assumptions that the corresponding linear system is approximately controllable. Using the fixed-point technique, fractional calculus and methods of controllability theory, a new set of sufficient conditions for approximate controllability of fractional integro-differential equations are form...

We study the effect of additive noise on integro-differential neural field equations. In particular, we analyze an Amari-type model driven by a Q-Wiener process, and focus on noise-induced transitions and escape. We argue that proving a sharp Kramers' law for neural fields poses substantial difficulties, but that one may transfer techniques from stochastic partial differential equations to esta...

The aim of this article is to present an efficient numerical procedure for solving mixed linear integro-differential-difference equations. Our method depends mainly on a Taylor expansion approach. This method transforms mixed linear integro-differentialdifference equations and the given conditions into matrix equation which corresponds to a system of linear algebraic equation. The reliability a...