Explicit solutions of the radial Schrödinger equation via fractional differintegral

This thesis consists of six main chapters. In chapter one; it is expressed a historical analysis, evolution, works found and usage fields of the fractional differintegral in summary. Furthermore, some fundamental definitions used in thesis are also given. In chapter two; The fundamental definitions, theories and properties of the fractional calculus theory are analyzed. Some definitions of the fractional differintegral that are usually used in applications, hypergeometric functions and Gauss differential equation are considered. In chapter three; Schrödinger equation and formation of its radial equation are given. Chapter four and chapter five form the original part of thesis. In chapter four; Some theorems are investigated. Explicit solutions of the radial equations in this theorems are obtained by means of suitable transformations and, suitable definitions and theories of the fractional calculus. Furthermore, hypergeometric forms of this fractional solutions are derived. In chapter five; solutions of the equations in chapter four are obtained via N- fractional calculus operator. In chapter six; obtained results are evaluated and open problems proposed in this subject are presented.