In this thesis the gamma distribution is considered for the reason of it’s appearance in many statistical fields of applications. Some mathematical and statistical properties of the distribution are collected and unified.
The main theme of this thesis is oriented toward three objectives.The first objective, is a study to fuzzy set theory with some basic properties related to differential equations.The second objective, is a study and prove of the existence and uniqueness theorem of fuzzy differential equations using two approaches, the first is by Brower fixed point theorem and the other by Schauder fixed point theorem.
The aim of this thesis is to prove the existence and uniqueness of the mild solutions of semilinear initial value control problems in a suitable Banach spaces as well as their controllability. Some theorems regarding controllability, local and global existence as well as uniqueness of the mild solution in infinite dimensional spaces have been developed in suitable Banach space using the Schauder fixed point theorem and the semigroup theory (compact semigroup).
