M.Sc.

The main aim of this work is to generalize the study of the one-dimensional integral equations to include the multi-dimensional integral equations.This study includes the classification of the multi-dimensional integral and integro-differential equations. Also, some extended theorems for the existence and uniqueness of solution for the multi-dimensional integral equations are given. Moreover, some generalized methods are used to solve the multi-dimensional integral equations, with some illustrative examples.

In this thesis, a new scheme and procedure for nonlinear dynamical control system design are proposed and developed. The proposed scheme is based on some suggested theorems. The proofs of the presented Theorems as well as their computational algorithm have been developed and presented. The concluding and necessary remarks have also been discussed. Some illustrations have also been implemented.