الفهرس 
Fuzzy Basics
Fuzzy differential equationsOnly 14 pages are availabe for public view
 |  | from | 128 |  |  |
| | | from | 128 | | |
Abstract
Preface Fuzzy differential equations have a wide popularity between researchers due to the smart applications and the uncertain environment values. The basic theory of fuzzy introduced by Zadeh till the coming of Hukuhara who has changed the identity of difference which affects the differentiability then these changes appeared in the differential equation. In this thesis, starting with chapter 1 which gives full background of the basic definitions of fuzzy numbers and the arithmetic operations applied on them with numerical examples to show the different method to apply these operations, then discussing Hukuhara theory and the reason of introducing the generalization of hukuhara theory, then move forward to next part which introduces the fuzzy function types and the integration theories. The theories of the differentiation and the affection of hukuhara difference definition on it, with estimated classes for nth order derivative. chapter 2 discusses the linear transformation approach to solve the fuzzy differential equations and introduce Gasilov method to solve the second order fuzzy differential equations then applied it on numerical examples in triangle and trapezoidal fuzzy numbers in the boundary conditions, But chapter 3 is an analytical solution of second order fuzzy differential equation in oscillatory equation form and under generalized Hukuhara differentiability, All general solution of all cases in all classes are collected in general table, illustrating examples are applied to show the solutions numerically. There are many numerical methods can be applied on fuzzy differential equation but chapter 4 uses finite difference method to solve the differential equation under generalized Hukuhara approach, then compare the results of approximate solution with the analytical one and by getting a good error rate, the study ended.