Thesis
SOLUTION OF CAUCHY TYPE PROBLEM OF PARTIAL FRACTIONAL ORDER DIFFERENTIAL EQUATIONS
In this work, we obtain an analytical solution for Cauchy type problem of partial fractional order differential equation in terms of Mittage – Leffler function using Laplace transformation. The existence and uniqueness of the analytical solution also, is reviewed by reducing the Cauchy type problem of partial fractional order differential equation into linear Volterra integral equation of the second kind and showing that the solution of our Cauchy type problem is equivalent to the solution of linear Volterra integral equation of the second kind.
Some Finite Difference Methods for Solving Fractional Differential Equations
The main purpose of this work is to study the numerical solutions for special types of the fractional differential equations via the finite difference methods with their stability. This study includes the following aspects:
Generating Normal Varieties by Monte Carlo Methods for Estimating the Cumulative Distribution Function and Parameters
This thesis consider the normal distribution with its important appearance in many statistical fields of applications. Some mathematical and statistical properties of the distribution have been collected and illustrated with moments and higher moments. Six related theorems have been studied in the applications of this type of distribution. The estimation manner and its properties have been illustrated throughout two methods (Moment and Maximum Likelihood methods) which are used to estimate the distribution parameters theoretically.
ORDER STATISTICS FOR TYPE II CENSORED EXPONENTIALLY DISTRIBUTED DATA IN ACCORDENCE OF EXPLANATORY VARIABLES
In this thesis, we consider a regression models for survival censored data of type II in which the underling distributions are exponential or gamma where the effect of the regressor variables on the means is multiplication given by the model Three methods of estimation for the regression coefficients are considered, namely maximum likelihood (ML), weighted least squares (WLS), and suggest weighted least squares (SWLS).
Nonlinear Dynamic Observer for Some Class of Nonlinear Singular Dynamic Control System
This work deals with the problem of dynamic state estimator for a class of non- linear singular dynamic systems.
On periodic boundary value problems of the ordinary integro-Differential Equations
The main aim of this work is classified into four objects, these are summarized as follows:
System Observer Design for Nonlinear Dynamic Control System and its Controller
The main theme of this thesis is the design of a full order nonlinear deterministic dynamic observer for estimation of state space from its nonlinear input-output dynamic control system.The quadratic Lyapunov function stabilization approach has been adapted and developed.The sufficient conditions for existence of the dynamic observer for some class of nonlinear input-output dynamic system have been presented and discussed. Useful linear transformations have also been adapted to design a stable controller based on the suggested dynamic (deterministic) observer system.
On the Multi-Dimensional Integral Equations
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
NONLINEAR DYNAMIC OBSERVER FOR A CLASS OF NONLINEAR DYNAMIC CONTROL SYSTEMS
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.
Nero-Controller of a Class of Uncertain Nonlinear Dynamical Control System
Today automatic control systems have become an integrated part of our life. They appear in every things from simple electronic household products to air planes and spacecrafts. Automatic control systems can take highly different shapes but common to them all, is their function to manipulate a system so that it behaves in a desired fashion.Control of nonlinear systems is a major application area for neural networks.