Notes on various operators of fractional calculus and some of their implications for certain analytic functions

Abstract

"The main purpose of this note is firstly to present certain information in relation with some elementary operators created by the well-known fractional calculus, also to determine a number of applications of them for certain complex function analytic in the open unit disc, and then to reveal (or point out) some implications of the fundamental results of this research. Keywords: Complex domains, open unit disc, normalized analytic function, fractional calculus, Operators of fractional calculus, Series expansions, inequalities in the complex plane. "