Thesis
MAGNITUDE ESTIMATION OF SOLUTIONS FOR SPECIAL TYPES OF DELAY DIFFERENTIAL EQUATIONS
The differential equations with a deviating argument are differential equations in which the unknown function and its derivative enter, generally speaking, under different values of the argument, [El'sgol'ts L. and Norkin S., 1973].These equations appeared in the literature in the second half of the eighteenth century by Kondorse in 1771, but a systematic study of equations with a deviating argument began only in the twentieth century (especially in the last forty years by Myshkis A. in the Soviet Union, Wright E. and Bellman R.
About the Stability of Fuzzy Differential Equations
Stability of fuzzy differential equations is one of the most important tasks in fuzzy set theory, since studying the behavior of the solution of the fuzzy differential system without solving the system explicitly fall into two categories:
On The Volume And Integral Points Of A polyhedron In
Computing the volume and integral points of a polyhedron in 
is a very important subject in different areas of mathematics. There are two representations for the polyhedron, namely the H-representation and the V-representation. For each representation we give a different method of finding the volume and number of integral points. Moreover, the Ehrhart polynomial of a bounded polyhedron is discussed with some methods for finding it.
Analytical Study and Approximated Methods for Solving Fractional Order Partial Differential Equations
This thesis is concerned basically with establishing theoretical background for the Riemann-Liouville definition of fractional differentiation and integration of the function of several variables and solving certain type of fractional partial differential equations using some approximated methods.
Functions Approximation Using G-Spline and its Generalization to Two-Dimensional Spaces
The first objectives of this thesis, is oriented towards function approximation using special type of spline, which is called the "G-spline" including the details of the subject and the proof of some lemmas and corollary for completeness. The second objective of this work is the generalization of G-spline functions for two-dimensional spaces including the statement and proof of the existence and uniqueness theorems as well as the statement and proof of the optimality of two-dimensional G-spline functions.
ON THE SOLUTIONS OF THE INTEGRAL INEQUALITIES
The integral inequalities have many applications in the mathematics, applications in the ordinary differential equations, partial differential equations, integro-differential equations, fractional differential equations, etc. From these applications, finding the global existence, uniqueness, stability of solutions and other types of applications.
NONLINEAR DYNAMIC CONTROL SYSTEMS DESIGN PROBLEM AND APPLICATIONS TO CHAOS
Non-linear differential equations appear prominently in the study of dynamical control systems, chaotic dynamical systems etc. Chaotic behavior study is very important in the nonlinear dynamical system theory and design.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.
Numerical Approximations To the Gamma Cumulative Distribution Function With Random Varietes Generation By Using Monte-Carlo Simulation
Fractional calculus is the subject of evaluating derivatives and integrals of non-integer orders of a given function, while fractional differential equations (considered in this work) is the subject of studying the solution of differential equations of fractional order, which contain initial conditions. The general form of a fractional differentia equation is given by:y(q) = f(x, y), y(q-k)(x0) = y0 where k = 1, 2, …, n + 1, n < q < n + 1, and n is an integer number.
Solution of Fuzzy Initial-Boundary Ordinary Differential Equations
One of the aims of study the fuzzy set theory is to develop the methodology of the formulations and the solutions of problems that are too complicated or ill-defined to be acceptable to analysis by conventioal techniques. Therefore, fuzziness could be considered as a type of imprecision that steams from a grouping of elements into classes that do not have exact defined boundaries. Such classes, introduced by Zadeh L. A., in 1965 as a tool used to describe the ambiguity, vagueness and ambivalence in the mathematical models.This thesis have three objectives.