الفهرس 
Chapter (1) UncertaintyOnly 14 pages are availabe for public view
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Abstract
On describing reality, uncertainty has many different meanings. Especially when trying to solve problems that are modelled in uncertainty and give a real solution instead of an ideal solution. In this research some differential equations will be solved in different models of uncertain environments by the use of various methods. To do that, we get the exact and approximate solutions of these equations to study the error estimates. The outline of the thesis is as follows: Chapter 1 provides a comprehensive overview of uncertainty and fuzziness. The first section delves into the fundamental definitions of uncertainty and highlights fuzziness as a significant form of uncertainty. The discussion further explores various types of fuzzy environments, beginning with the concept of fuzziness and progressing to intuitionistic fuzzy and Neutrosophic fuzzy environments. Additionally, the chapter is devoted to give the definition of uncertain numbers and presents different approaches for modelling them within the context of fuzziness. Furthermore, the chapter introduces the concept of uncertain numbers in mixed fuzzy environments. In the subsequent section of this introductory chapter, we will examine the concepts of arithmetic operations and Hukuhara theory. Following this, fuzzy function definitions and types are given. This will serve as a foundation for introducing ideas related to fuzzy integration and differentiation. Besides, the concept of a differential equation in an uncertain environment is discussed and then various methods to solve them are introduced. Chapter 2 presents an analytical solution for a second-order differential equation in the form of an oscillatory equation. This solution is applicable in an uncertain environment and considers generalized Hukuhara differentiability. Besides, the chapter covers all solutions for different coefficient signs within the four classes of generalized Hukuhara. Additionally, numerical examples are provided to demonstrate the application of fuzzy, intuitionistic fuzzy, and Neutrosophic fuzzy environments in modeling uncertain scenarios. There are numerous numerical approaches that can be employed for solving fuzzy differential equations. However, in chapter 3, the finite difference method is utilized to solve fuzzy differential equations using the modified Hukuhara approach. The obtained approximate solution is then compared with the analytical solution in order to analyze error estimates.