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. Furthermore, the analytical and numerical solutions of some namely fuzzy differentials equations are given.The third objective, is to study the real life application, which is modeling and solution of the decay of the biochemical oxygen demand in water using fuzzy set theory, as well as, the numerical solution and compared with the exact solution.
