The Existence and Uniqueness of Solution of a Neutral Functional Differential Equation

Up to now, many things were said about differential equations without time delay, the so called

ordinary differential equations or partial differential equations, and their solutions. The fixed point

theorems have been used to show the existence and unique

ness of solution of initial value problem of

these equations. Since time delay occurs naturally in just about every interaction of the real world,

here in this paper we see some differential equations with time delay, the so called functional

differential equations or delay differential equations. In general, we used Banach Cacciopoli

Theorem and Schauder’s fixed point theorem to show the existence and uniqueness of solution of a

neutral functional differential equation.