An extensive note on various fractional-order type operators and some of their effects to certain holomorphic functions

Abstract

The aim of this paper is to present background information in relation with some fractional-order type operators in the complex plane, which is designed by the fractional-order derivative operator(s). Next we state various implications of that operator and then we show some interesting-special results of those applications.

Keywords

• complex plane
• holomorphic function
• series expansion
• fractional-order calculus
• operators in certain domains
• argument properties