Mathematics and Computer Applications - Sciene

The main purpose of this work is to study Volterra-Fredholm integral and integro-differential equations. This study include the classification of Volterra-Fredholm integral and integro-differential equations.Also, some theorems for the existence and uniqueness of the solution for linear Volterra-Freadholm integral and integro-differential equations are presented. Moreover, Taylor expansion method for solving special types of nonlinear Volterra-Freadholm integral and integro-differential equations with some illustrate examples are discussed.
 

In this work we consider the Inverse Gaussian distribution model of two parameters, because it have many applications in the fields of statistics and reliability. Mathematical and statistical properties of the distribution are given together with illustration. Moments and higher moments of the distribution properties and of the reliability and hazard functions are discussed theoretically. Two methods of estimation namely moments method and maximum likelihood method are used to estimate the distribution parameters.

The objective of this work may be oriented toward two objectives.The first objective is to study fuzzy set theory, as well as some of its basic algebraic properties and theoretical results.The second objective is to study D-metric spaces and M-fuzzy metric spaces, and some of their properties. Also, this objective includes the study of complete fuzzy metric spaces using M-fuzzy distance function. In addition, some additional results are presented and proved in this work.