On invariants of surfaces with fractional order

Forthe last decade, using the techinques of fractional calculus in the differential geometric theories has been an interesting field. As a first step, in the context of this thesis, the notion of local surface of fractional order is introduced. Following this notion, the local surfaces of fractional order are characterized by their second fundamental form of fractional order. Clearly, it is obtained that a local surface of fractional order is geometrically a part of plane when the components of second fundamental form of fractional order vanish identically. In the last part, examples are solved for different α values. This coincides with the classical situation.