M.Sc.

Non-linear differential equations appear prominently in the study of dynamical control systems, chaotic dynamical systems etc. Chaotic behavior study is very important in the nonlinear dynamical system theory and design.In this thesis, a new scheme and procedure for nonlinear dynamical control system design are proposed and developed. The proposed scheme is based on some suggested theorems. The proofs of the presented Theorems as well as their computational algorithm have been developed and presented.

Fractional calculus is the subject of evaluating derivatives and integrals of non-integer orders of a given function, while fractional differential equations (considered in this work) is the subject of studying the solution of differential equations of fractional order, which contain initial conditions. The general form of a fractional differentia equation is given by:y^(q) = f(x, y), y^(q-k)(x₀) = y₀ where k = 1, 2, …, n + 1, n < q < n + 1, and n is an integer number.

One of the aims of study the fuzzy set theory is to develop the methodology of the formulations and the solutions of problems that are too complicated or ill-defined to be acceptable to analysis by conventioal techniques. Therefore, fuzziness could be considered as a type of imprecision that steams from a grouping of elements into classes that do not have exact defined boundaries. Such classes, introduced by Zadeh L. A., in 1965 as a tool used to describe the ambiguity, vagueness and ambivalence in the mathematical models.This thesis have three objectives.