Abstarct: The main topic of this thesis is studying the applications of fuzzy systems to solve fractional differential algebraic equations and related problems. Some dynamic and physical laws are not expressed in general dynamical systems. For modeling complex systems or when the particles are in microscopic scales, the use of fractional order systems seems to be essential. Obtaining analytical solutions for such problems is usually difficult.Therefore, numerical methods for obtaining the approximate solutions of these equations, have been proposed. In this thesis, fuzzy system is used for the numerical solution of variable-order fractional differential algebraic equations and fractional optimal control problem. Fuzzy logic system is an artificial intelligent technique that uses a collection of fuzzy membership functions and rules, instead of Boolean logic, to reason about data. Fuzzy systems can provide a more transparent representation of the studied system, comparing with the popular approximation methods such as artificial neural networks. Existence of this merit in fuzzy systems, is due to the possible linguistic interpretation in the form of rules. Since the fuzzy system is universal approximator, this approach of the computational intelligence has been used for a wide variety of applications.