Mathematics and Computer Applications - Sciene

       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.

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:

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.