Examination of curves with the aid of fractional derivatives

Fractional analysis has a great importance in the theoretical part of mathematics as well as in the field of application. In this thesis, the geometry of curves will be discussed using Fractional Analysis techniques. While doing this, the Caputo fractional derivative operator will be discussed among the fractional derivative operators. The aim of this study is to contribute to the geometrical equivalents of the fractional derivative thanks to the fractional tangent and normal vector fields of a level curve. The concepts of fractional tangent and normal vector fields of a level curve are defined. The relations between these and standard concepts were examined.