Interpreting the geometry of magnetic field lines near null points with fractional derivation

In this thesis, the characterization of the null (neutral) points of the magnetic field is given using the Caputo fractional calculation method in 3-dimensional Euclidean space. Then, by reformulating the numerically solved boundary initial value problem, magnetic reconnection states and the behavior of magnetic field lines around null points are analyzed. Killing magnetic vector fields are calculated according to the Caputo fractional calculation method, and the charged particle movement around these magnetic field lines is characterized. Then, magnetic surfaces called flux tubes, which accept these magnetic field lines as parameter curves, are examined. In addition, the results obtained are visualized with the help of mathematical programs and compared with the results obtained with integer and fractional calculations. The first part of the thesis, which consists of six chapters, consists of an introduction where the studies on the subject mentioned in the thesis and the motivation of what is done in this thesis are explained. In the second chapter, mathematical and physical definitions, theorems, and lemmas used in preparing the thesis are included. In the third, fourth, and fifth chapters, which constitute the original part of the thesis, the characterization of null points and the behavior of magnetic field lines near null points are examined using the Caputo fractional analysis method. Magnetic reconnection has been investigated according to the magnetohydrodynamic equation. Additionally, the Killing magnetic field is calculated by the Caputo fractional analysis method. Then, the curves obtained by the movement of a charged particle in the Killing magnetic field are analyzed by the Caputo calculation method. Additionally, magnetic surfaces called magnetic flux tubes have been obtained, which accept the magnetic field lines around null points as generating curves. Additionally, the magnetic flux tube surfaces are classified thanks to the eigenvalues of the matrix form associated with the magnetic field lines. Finally, examples confirming the results are given and visualized with the help of mathematical programs. In the sixth chapter, which is the last part of the thesis, the results obtained are interpreted geometrically and physically.