الفهرس 
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Abstract
Our aim in this thesis is to discuss fractional formalism of high temperature superconductivity and to propose a model on fractional order high temperature superconductivity. The thesis is divided into three chapters: Chapter one is an introductory chapter where we present a general introduction to the problem, some well-known definitions such as superconductivity, entanglement, fractional calculus and some well-known results and background material that are used in this thesis such as application of high temperature superconductivity. In chapter two, we discuss fractional formalism of fractional order of high temperature superconductivity and propose a model on fractional order of high temperature superconductivity; at the end of this chapter we illustrate that, we need two interactions to explain high temperature superconductivity, we explain why we use fractional order to explain high temperature superconductivity and we mentioned at the end of the chapter that, the strong interactions can be described by using fractional order nonlinear Schrodinger equation. In chapter three, we discuss some of the models for high temperature superconductivity, such as Alexandrov model, E.Ahmed model in 1990 and Anderson model. At the end of this chapter, we obtained that, the solution for fractional order nonlinear Schrodinger equation by using homotopy perturbation method. Finally, a summary for the entire thesis is presented.